ABSTRACT Title of Document: ELECTRONIC PART TOTAL COST OF OWNERSHIP AND SOURCING DECISIONS FOR LONG LIFE CYCLE PRODUCTS Varun Jonathan Prabhakar, Doctor of Philosophy, 2011 Directed By: Professor Peter Sandborn, Department of Mechanical Engineering The manufacture and support of long life cycle products rely on the availability of suitable parts from competent suppliers which, over long periods of time, leaves parts susceptible to a number of possible long-term supply chain disruptions. Potential supply chain failures can be supplier-related (e.g., bankruptcy, changes in manufacturing process, non-compliance), parts-related (e.g., obsolescence, reliability, design changes), logistical (e.g., transportation mishaps, natural disasters, accidental occurrences) and political/legislative (e.g., trade regulations, embargo, national conflict). Solutions to mitigating the risk of supply chain failure include the strategic formulation of suitable part sourcing strategies. Sourcing strategies refer to the selection of a set of suppliers from which to purchase parts; sourcing strategies include sole, single, dual, second and multi-sourcing. Utilizing various sourcing strategies offer one way of offsetting or avoiding the risk of part unavailability (and its associated penalties) as well as possible benefits from competitive pricing. Although supply chain risks and sourcing strategies have been extensively studied for high-volume, short life cycle products, the applicability of existing work to long life cycle products is unknown. Existing methods used to study part sourcing decisions in high-volume consumer oriented applications are procurement-centric where cost tradeoffs on the part level focus on part pricing, negotiation practices and purchase volumes. These studies are commonplace for strategic part management for short life cycle products; however, conventional procurement approaches offer only a limited view for parts used in long life cycle products. Procurement-driven decision making provides little to no insight into the accumulation of life cycle cost (attributed to the adoption, use and support of the part), which can be significantly larger than procurement costs in long life cycle products. This dissertation defines the sourcing constraints imposed by the shortage of suppliers as a part becomes obsolete or is subject to other long-term supply chain disruptions. A life cycle approach is presented to compare the total cost of ownership of introducing and supporting a set of suppliers, for electronic parts in long life cycle products, against the benefit of reduced long-term supply chain disruption risk. The estimation of risk combines the likelihood or probability of long-term supply chain disruptions (throughout the part?s procurement and support life within an OEM?s product portfolio) with the consequence of the disruption (impact on the part?s total cost of ownership) to determine the ?expected cost? associated with a particular sourcing strategy. This dissertation focuses on comparing sourcing strategies used in long life cycle systems and provides application-specific insight into the cost benefits of sourcing strategies towards proactively mitigating DMSMS type part obsolescence. ELECTRONIC PART TOTAL COST OF OWNERSHIP AND SOURCING DECISIONS FOR LONG LIFE CYCLE PRODUCTS by Varun Jonathan Prabhakar Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2011 Advisory Committee: Professor Peter Sandborn, Chair Professor Shapour Azarm Professor Wedad J. Elmaghraby Professor Jeffrey W. Herrmann Professor Santiago Solares ? Copyright by Varun Jonathan Prabhakar 2011 ii Dedication I would like to dedicate this dissertation to my wonderful family for their love and unwavering support. I would also like to dedicate this work to all my friends, colleagues, professors and staff members who have been a perpetual source of motivation and inspiration over the past five years. iii Acknowledgements I would like to acknowledge my advisor and mentor, Professor Peter Sandborn, for his support and guidance. I would also like to thank the more than 100 companies and organizations that support research at the Center for Advanced Life Cycle Engineering (CALCE) at the University of Maryland annually. Specifically, I would like to acknowledge CALCE members, Ericsson AB, Textron and SiliconExpert, for the valuable feedback and insight into the practical applications of the methodology presented in this dissertation. iv Table of Contents Dedication ..................................................................................................................... ii Acknowledgements...................................................................................................... iii Table of Contents......................................................................................................... iv Nomenclature............................................................................................................... vi List of Figures ............................................................................................................ viii List of Tables ............................................................................................................... xi Chapter 1: Introduction ................................................................................................. 1 1.1 Background ......................................................................................................... 5 1.1.1 Supply chain failure ..................................................................................... 5 1.1.2 Part sourcing strategies ................................................................................ 8 1.1.3 Electronic part management organizations................................................ 15 1.1.4 Long life cycle vs. short life cycle products .............................................. 16 1.1.5 DMSMS type part obsolescence................................................................ 18 Chapter 2: Dissertation scope and problem statement................................................ 21 2.1 Problem Statement ............................................................................................ 21 2.1.1 Dissertation Scope ..................................................................................... 21 2.1.2 Research overview..................................................................................... 24 2.2 Technical tasks.................................................................................................. 28 Chapter 3: Part sourcing total cost of ownership (TCO) ............................................ 30 3.1 Part TCO model for single sourcing ................................................................. 31 3.1.1 Support cost model .................................................................................... 34 3.1.2 Assembly cost model ................................................................................. 37 3.1.3 Procurement and inventory cost model...................................................... 40 3.1.4 Field failure cost model ............................................................................. 42 3.2 Modifications to address multi-sourcing .......................................................... 43 3.2.1 Support cost model .................................................................................... 47 3.2.2 Assembly cost model ................................................................................. 50 3.2.3 Procurement and inventory cost model...................................................... 52 3.2.4 Field failure cost model ............................................................................. 53 3.2.5 Disruption resolution (re-qualification) ..................................................... 54 3.3 Evaluating part TCO......................................................................................... 56 3.3.1 Part TCO example case study (SMT capacitor) ........................................ 56 3.4 Discussion and conclusions .............................................................................. 66 Chapter 4: Forecasting long-term supply chain disruptions due to DMSMS type obsolescence ............................................................................................................... 68 4.1 DMSMS obsolescence forecasting ................................................................... 69 4.1.1 Procurement life forecasting ...................................................................... 70 4.1.2 Electronic part obsolescence data .............................................................. 72 4.1.3 Determining mean procurement lifetimes ................................................. 73 4.2 Supplier-specific obsolescence likelihood (MLE)............................................ 81 4.3 Summary and discussion................................................................................... 83 Chapter 5: Long-term sourcing risk model (DMSMS obsolescence)......................... 86 5.1 Part sourcing risk .............................................................................................. 87 v 5.1.1 Linear regulator case study ........................................................................ 88 5.3 Summary and discussions ................................................................................. 97 Chapter 6: Analytical part TCO model....................................................................... 99 6.1 Problem statement............................................................................................. 99 6.2 Model assumptions and formulation............................................................... 101 6.3 Comparison of sourcing strategies.................................................................. 104 6.4 Comparison of analytical and simulation part TCO models (part TCO)........ 110 6.5 Implementation of analytical part TCO model (break-even learning index).. 113 Chapter 7: Summary and contributions .................................................................... 125 7.1 Summary......................................................................................................... 125 7.2 Conclusions and contributions........................................................................ 125 7.3 Future work..................................................................................................... 131 Appendix A ? Design reuse ...................................................................................... 135 A.1 Design reuse of electronic components subject to long-term supply chain disruptions............................................................................................................. 135 A.2 Summary and discussions .............................................................................. 144 Appendix B - Part lifetime buy tradeoffs.................................................................. 145 B.1 Lifetime buy analysis ? buffer size analysis using part TCO ........................ 146 B.2 Summary and discussions .............................................................................. 149 Appendix C - Supplier-specific obsolescence likelihood (numerical method) ........ 150 References................................................................................................................. 153 Curriculum Vitae ...................................................................................................... 164 vi Nomenclature Bx = supplier learning index for corresponding support activity x BTH = learning index threshold Cx = support costs for support activity vector x, i.e., Cia, Cpa, Cas, etc. Cproc = annual part procurement cost (exclusive of inventory) Crepair = cost of repair per product instance Creplace = cost of replacing the product per product instance CVAR = cost of product-related resolutions as a function of NPROD CFIXED = fixed component of disruption resolution cost wrC = cost of processing the warranty returns TCOC = part total cost of ownership (TCO) CPPS = part TCO per part site expC = average expected cumulative TCO per part site sD = effective disruption date (obsolescence date) of a part procured through sourcing strategy s f(t) = PDF value of procurement life at time t F(t) = CDF value of procurement life at time t failf = number part failures from supplier p calculated from supplier-related frep = fraction of failures requiring replacement (as opposed to repair) of the product FIT rates (assuming a constant failure rate) Foverbuy = overbuy (buffer) quantity as fraction of lifetime buy quantity h = holding/storage/inventory cost per part per year i = year index (starting at 1) j = end of part?s support life cycle (years after start) KTH = ratio (threshold) of support cost for repeated support activities in sourcing strategy b with respect to support cost in single sourcing strategy a LP = part procurement life (years) n = length of support activity vector x TN = number of part procured for assembly in a particular VOLN = number of parts sites for assembly PROC pN = number of parts procured from supplier p PRODN = number of product designs that the part is used in failN = number of failures under warranty SUP sN = number of suppliers involved in sourcing strategy s p = supplier index SUP pP = part price from supplier p Q = part quantity in storage/inventory vii r = discount rate on money ?p = fraction of total part usage that is purchased from supplier p G pVol = number of good parts before assembly process from supplier p, i.e., parts free from defects Volp = volume of parts procured from supplier p viii List of Figures Figure 1.1 ? Taxonomy of general supply chain disruptions (includes long-term and short-term disruptions). Figure 1.2 ? Manufacturer (supplier) assessment process flow (Pecht 2004). Figure 1.3 ? The total number of discontinuance notices (notices from the original manufacturer that manufacturing of the part will be terminated) for electronic parts in years 2006-2009 from SiliconExpert Technologies, Inc. databases. Figure 3.1 ? Test/diagnosis/rework (TDR) model from Trichy et al. (2001). Table 3.1 describes the notation appearing in this figure. Figure 3.2 ? Inputs used in the basic part total cost of ownership cost model for the examples provided in this chapter. Figure 3.3 ? Example (top) part usage profile per product and (bottom) total part and product usage over time for the high-volume cases provided in this chapter. Figure 3.4 ? Example part cost of ownership modeling results (high-volume case). Figure 3.5 ? Part total cost of ownership results for different part volumes (low volume cases). Figure 3.6 ? Part TCO results vs. procurement price for low volume case (total part usage of 49,752 parts). Figure 3.7 ? Part TCO results vs. procurement price for high volume case (total part usage of 49,753,000 parts). Figure 3.8 ? Tornado Chart of cost impact as change in total effective cost per part site due to ?20% variability in input values. Figure 4.1 ? Procurement life (LP) as a measure for length of a part?s procurement life cycle. Figure 4.2 ? 347 obsolete linear regulators from 33 manufacturers. DA = 2008, the analysis date (the date on which the analysis was performed). Figure 4.3 ? The distribution of procurement lifetimes for linear regulators. The histogram on the left side corresponds to the data in Figure 4.2. The mean procurement lifetime (censored) = 11.63 years, ? = 2.84, ? = 13.06. The parameters are based on a maximum likelihood estimate (MLE) using a two-parameter Weibull fit. Figure 4.4 ? Hazard rate corresponding to the censored distribution of procurement lifetimes for linear regulators in Figure 4.3. Figure 4.5 ? Quantity and percentage of linear regulators that are not obsolete as of 2008 as a function of time. Figure 4.6 ? Mean procurement lifetime for linear regulators as a function of time (parts introduced on or before the date). Figure 4.7 ? Mean procurement lifetime for linear regulators as a function of time (parts introduced on the date). Note, there were no parts introduced in 1993. ix Figure 4.8 ? Supplier-specific procurement life data for linear regulators (ON Semiconductor): (A) raw obsolescence data from SiliconExpert; (B) censored PDF and CDF of obsolescence risk likelihood over time. Figure 5.1 ? Part TCO model inputs used in the example linear regulator case study (total production volume = 10,500 part sites). Figure 5.2 ? Supplier-specific obsolescence likelihoods for linear regulators as (top) PDF and (bottom) CDF determined from historical data provided by SiliconExpert. The resulting Weibull fits are given in Table 5.1. Figure 5.3 ? Cexp over time for single sourcing (price-independent case for linear regulator example). Figure 5.4 ? Cexp over time for single sourcing (price differences included for linear regulator example). Figure 5.5 ? (left) CDF of obsolescence likelihood by sourcing strategy and (right) annual expected cumulative TCO per part site over time by sourcing strategy (price independent case for linear regulator example). Figure 5.6 ? CDF of obsolescence likelihood by sourcing strategy (linear regulators). Figure 6.1 ? Plot of break-even learning index, BBE, with respect to the ratio, K = ?CTCO/Csup, at break-even (where TCO of a sourcing strategy with SUP bN number of suppliers is equal to the TCO of single sourcing). Figure 6.2 ? Error between the simulation and analytical part TCO models as difference in TCO (as a fraction of average TCO determined from the simulation and analytical part TCO models), with respect to the average procurement and inventory cost (as fraction of average TCO) for a low volume case (49,752 parts) and a high volume case (49,753,000 parts). Figure 6.3 ? Cost difference (per part site) between part TCO, CTCO and procurement/inventory cost, Cproc/inv with respect to total part usage volume after 20 years. Figure 6.4 ? Inputs for the example case discussing the method in Section 6.3 (Lp is the part?s effective procurement life and DI is the part?s introduction date). Figure 6.5 ? Part TCO (per part site) versus year of support for the example case where inventory cost is $0.1 per part. Figure 6.6 ? Part TCO (per part site) versus year of support for the example case where inventory cost is $10 per part. Figure 6.7 ? Part TCO (per part site) versus year of support for the example case where learning index, B is 0 (maximum allowable inventory cost is $3.84 per part). Figure 6.8 ? Break-even learning index, BBE versus inventory cost (per part per year) for the low volume example case discussed in Figure 6.4. Figure 6.9 ? Break-even learning index, BBE versus inventory cost (per part per year) with contour lines of varying procurement price for the low volume example case discussed in Figure 6.4. x Figure 6.10 ? Fraction of support cost repeated for second supplier (with respect to single sourcing support cost) at break-even, KBE vs. inventory cost (per part per year) with contour lines of varying procurement price for the low volume example case discussed in Figure 6.4. Figure 6.11 ? Monte Carlo results for inventory cost of $1 (per part per year) - probability of occurrence of KBE (CDF). Figure 6.12 ? Monte Carlo results for inventory cost of $1 (per part per year) - probability that KBE exceeds KTH. Figure 6.13 ? Monte Carlo results for inventory cost of $10 (per part per year) - probability that KBE exceeds KTH. Figure 6.14 ? Monte Carlo results for inventory cost of $100 (per part per year) - probability that KBE exceeds KTH. Figure A.1 ? (left) 1 to 20 products concurrently using the example part described in Figure 3.2 and Figure 3.3. No finite resource limited problems. (right) annual cost per part site of design reuse in 1 product and 20 products. Figure A.1 ? (left) 1 to 20 products concurrently using the example part described in Figure 3.2 and Figure 3.3. No finite resource limited problems. (right) annual cost per part site of design reuse in 1 product and 20 products. Figure A.2 ? 1 to 20 products concurrently using the example part described in Figure 3.2 and Figure 3.3. Problem introduced in year 5 (left) and year 10 (right). Figure A.3 ? Optimum number of products using a common part with respect to problem resolution commonality. Total quantity of each part = 12,910,500. Figure A.4 ? Weighted total effective cost per part site of a fixed pool of 20 products. Problem introduced in year 5. Figure A.5 ? 1 to 20 products concurrently using the example part described in Figure 3.2 and 3.3. Problem introduced in year 5, total quantity of each product = 12,910. Figure B.1 ? Cumulative cost per part site as a function of part procurement life (YTO) for (left) 0% and 10% overbuy on lifetime buys, and (right) 10% overbuy with respect to cost category. Figure C.1 ? Steps in the process of generating a custom CDF/PDF from supplier- specific procurement life data for linear regulators (ON Semiconductor): (A) raw obsolescence data (B) ordered procurement life data (C) CDF of obsolescence from sampled procurement life data for a population size of N = 1000 (D) PDF and CDF of obsolescence risk likelihood over time calculated at one year intervals. xi List of Tables Table 3.1 ? Example matrix of the characteristics of various support activities x. Table 3.2 ? Nomenclature used in Figure 3.1. Table 3.3 ? Example matrix for the number of suppliers, SUPsxN for which support cost components x are applicable with respect to various sourcing strategies. Table 4.1 ? Procurement lifetimes for various electronic part types through 2008. ? and ? refer to 2 parameter Weibull fits of the censored and uncensored PDFs. LKV is the negative log-likelihood function (larger negative values indicate a better fit). Table 5.1 ? Supplier-specific censored Weibull distribution parameters, ? and ?. LKV is the negative log-likelihood function (larger negative values indicate a better fit). 1 Chapter 1: Introduction In today?s market, materials and goods flow through a complex network of organizations called ?supply chains? on their way to becoming a finished product. Original Equipment Manufacturers (OEMs) are product manufacturers that purchase or fabricate lower-level parts and integrate them into products that bear the organization?s name. Each OEM interacts with suppliers and customers through the transaction of goods where the assembly of products relies on the availability of suitable parts with sufficient attributes from competent suppliers. An OEM organization?s reliance on the external procurement of necessary parts leaves it susceptible to supply chain risk. Consider the following example: On March 17th, 2000, a lightning bolt caused by a thunderstorm struck electric power lines feeding to Philips? chip-manufacturing plant in Albuquerque, New Mexico (Latour 2001). A small fire erupted that was extinguished by the automatic sprinkler system within ten minutes. The building suffered only minor damage but the production of chips was shut-down for three weeks. Thousands of semiconductor chips being fabricated at the plant were destroyed by water damage while the debris and smoke particles from the fire compromised the sterile environment contaminating millions of chips in storage. Six months later, Philips was only able to return to producing half the capacity it was producing before the incident. The overall damage caused by the fire at Philips was, in fact, far more severe than expected. Ericsson, a leading cell-phone manufacturer at the time, purchased many of its chips from Philips exclusively. According to Ericsson?s statement in 2001, the drastic reduction in production and sales attributed to the shortage of millions of chips, many of which 2 were expected to be used in important new products, cost the company more than $400 million. That year, Ericsson?s mobile phone division alone lost $1.7 billion for a variety of reasons related to the fire at Philips and eventually withdrew from manufacturing mobile phones. On the other hand, Nokia, a Finnish competitor to Ericsson in the communications industry who attributes 70% of its $20 billion annual revenue to mobile phones, purchased chips from Philips as well. In fact, semiconductor procurement from Nokia and Ericsson together accounted for 40% of Philips? production. Following the incident at Philips, Nokia mobilized alternative sources, diverted capacity from other U.S. and Japanese suppliers, and managed to continue production with nearly no consequences (Waters 2007). The assessment and mitigation of supply chain risk are critical to maintaining a robust supply chain and have been extensively studied in literature, including systems devised by Ericsson following Philips? incident (Norman and Jansson 2004). Events that lead to potential supply chain failures can be supplier-related (bankruptcy, changes in manufacturing process, non-compliance), parts-related (obsolescence, reliability, design changes), logistical (transportation mishaps, natural disasters, accidental occurrences) and political/legislative (trade regulations, embargo, national conflict). Part of the solution to mitigating the risk of supply chain failure is the strategic formulation of suitable part sourcing strategies. Utilizing various sourcing strategies offer ways of offsetting or avoiding penalties associated with part unavailability as well as possible benefits from competitive pricing. Large electronics OEMs, such as Ericsson, Motorola, and Honeywell, have dedicated electronic part management groups that are responsible for identifying, 3 selecting, qualifying, and purchasing electronic parts for specific products as well as qualifying the manufacturers and distributors of those parts. Often, electronic systems OEMs maintain databases that consist of hundreds of thousands of electronic parts (Pecht 2004). Part management tasks performed on a regular basis include determining the procurement status of parts, managing purchase orders, and part database maintenance. These tasks require considerable resources throughout the part?s existence within the database. Assessing and mitigating supply chain risk is one of the responsibilities of these part management groups. Unfortunately, part selection for products is often driven or significantly influenced by procurement management processes that have little or no view into the effective cost of ownership or through-life cost ramifications of the part. Procurement organizations are often motivated by minimizing procurement cost or selecting suppliers that offer parts at lower prices, and may not take into account many of the part selection and management group?s activities listed above (or more importantly, how the cost of these activities may vary from part-to-part). Price has long been considered a driving factor in purchases (Evans 1981, Lehmann and O?Shaughnessy 1974) but more recent studies have shown that price has declined in relative importance as a selection criterion (Jackson 1985, Wilson 1994). A survey study by Bharadwaj (2004) found that, out of four key supplier selection criteria ? delivery, price, quality, and post-sale service ? price was indeed the penultimate decision criteria used by electronic component procurement organizations followed by post-sales service. The study by Bharadwaj also suggests that differences do not exist within the buying criteria across an array of electronic components. However, 4 the implications of such policies and the impact of these decision criteria are yet to be explored. Electronic products can be categorized into long life cycle and short life cycle products. Popular consumer electronics, such as computers, mobile phones, GPS (global positioning systems), and so on, have relatively short procurement lives since they become obsolete within a few years of their market introduction (usually 5 years or less) . On the other hand, long life cycle products, such as those used in aerospace, military, communications infrastructure, power plants, and medical applications, remain in use and must be supported for significantly longer (often 20 years or more). Long life cycle products must utilize electronic parts procured from the same supply chain as short life cycle products resulting in a high frequency of part obsolescence1. As a result, the management of parts used in long life cycle electronic products differs from their short life cycle counterparts. Although supply chain risk has been extensively studied, the applicability of existing work to long life cycle products is limited. Existing methods used to study part management decisions are procurement-centric where cost tradeoffs on the part level focus only on part pricing, negotiation practices and purchase volumes. These studies are commonplace in strategic part management for short life cycle products; however, conventional procurement approaches offer only a limited view in the assessment of parts used in long life cycle products. Procurement-driven decision making provides little to no insight into the accumulation of life cycle cost (attributed to the adoption and use of the part), which can be significantly larger than 1 Integrated circuit fabrication facilities cost $1 Billion or more today. Long field life product sectors generally do not consume enough electronic parts to justify owning their own fabrication facilities or to support a dedicated electronic part supply chain. 5 procurement costs in long life cycle products. Therefore, a life cycle cost approach is necessary to assess part management decisions in long life cycle products. 1.1 Background This section discusses the characterization of various sources of supply chain risk. A background into supplier risk management is presented that justifies the need for new methods in part management suitable for managing parts used in both short and long life cycle products. This section also provides an overview of various sourcing strategies that are commonly employed to mitigate supply chain risk. Finally, the characteristics of electronic part management groups within electronic OEM organizations and the differences between long life cycle and short life cycle electronic products are described. 1.1.1 Supply chain failure A supply chain for a specific part or component is often made up of a network of several OEMs. Each OEM relies on part suppliers leaving the organization vulnerable to events that affect the intended functioning of the supply chain. Some forms of supply chain failures discussed in literature include (Gaonkar and Viswanadham 2004): (1) Deviation ? a deviation occurs when certain performance measures are affected by one or more parameters (e.g., cost, demand, lead-time) straying from expected or mean values without affecting the supply chain structure. (2) Disruption ? a disruption is an unexpected event that causes a radical transformation in the supply chain structure. Supply chain disruptions affect part 6 procurement through supplier or part unavailability, warehousing, distribution facilities or transport options. Supply chain disruptions are usually a result of events such as natural disasters, shipment delays, and non-compliant suppliers to name a few. Two types of supply chain disruptions can occur: i. Short-term disruptions are temporary problems that usually only affect a limited number of products that share the part for a short period of time, e.g., you receive a bad batch or lot of parts, or this week?s delivery of parts is going to be two days late. ii. Long-term disruptions refer to problems that make it impossible for an organization to continue using the part, e.g., reliability issues, changes made to the part by the part manufacturer, or the part becomes un-procurable (obsolete). Long- term problems such as a fundamental supply chain or wear out problem affects all products that share the part and require that a permanent solution (often a replacement part) must be found. Examples of long-term part supply problems are discontinuance of the part (obsolescence), supplier unavailability, functional design errors, counterfeit part issues, and part reliability problems. (3) Disaster ? a disaster is a temporary but irrecoverable shut down of the supply chain system due to unforeseen catastrophic system-wide disruptions. Disasters may be a result of a number of supplier disruptions or a single common-mode2 disruption of sizeable magnitude. Disruptions and disasters differ from deviations in severity, consequences and level of management required to mitigate the supply chain failure. Deviations are 2 A common-mode disruption is a supply chain failure of more than one supplier caused by a specific event (or an identical set of events). For example, alterations in trade policies may affect all offshore suppliers for a particular part in the same way. 7 mitigated on the tactical or operational level while disruptions and disasters are managed on a strategic level. Disruptions may occur internally or externally (Figure 1.1). External disruptions are events outside the realm of the OEM control, which prevent the use of a part. External disruptions can be generally categorized by causes into: 1) political and legal, 2) supplier related, 3) part related, and 4) logistical disruptions. Internal disruptions are events that occur within the OEM organization, which affect the assembly of parts into products. Resolutions of internal disruptions are more likely to be under the control of the OEM while external disruptions require the supply chain to be restructured. The assembly of products by an OEM organization is subject to supplier related problems that affect how an OEM procures their parts. The result is Political and Legal Trade policy Breach of security Corporate structuring Supplier Related Non-compliance (Eg. Quality) Breach of trust Bankruptcy Obsolescence Evolution of Manufacturing Process Natural disasters and accidents Part related Evolution of design Dormant part issues and vulnerability Logistical Transit Port closures Communication Internal Equipment or process Power outages Natural disasters Accidental occurrences Disruptions External Figure 1.1 ? Taxonomy of general supply chain disruptions (includes long-term and short-term disruptions). 8 an alteration in the intended supply chain structure or a supply chain disruption. Relevant supply chain issues and their categorization are depicted in the taxonomy shown in Figure 1.1. 1.1.2 Part sourcing strategies Supply chain risk management can be divided into three categories (Gaonkar and Viswanadham 2004): ? Tactical ? day to day management of activities ? Operational ? task specific management ? Strategic ? organizational level management of interacting groups Management on each of the three levels is vital to the proper functioning of part management organizations. Strategic management allows part management groups within OEMs to manage resources proactively in order to limit damages and cost penalties attributed to supply chain disruptions. A large body of research (discussed in this section) addresses part sourcing strategies as a valid supply chain risk mitigation approach. Part sourcing strategies are a common method of mitigating supply chain risks. A part sourcing strategy is a supply chain configuration that describes the number of suppliers from which to purchase parts and how they will be used during the period that the part exists in the OEMs database. Several sourcing strategies may be utilized to prevent the shortage of parts. Part sourcing strategies may be formulated to use more than one supplier or support backup suppliers from which to purchase parts should the primary supplier fail to meet demand (commonly referred to as ?demand switching?). However, introducing suppliers and parts into the parts 9 database involves additional resources and cost. Therefore, for efficient database management, the part manager is responsible for tradeoff decisions that determine the use of parts across multiple products and the use of suppliers over the part?s life cycle. These decisions have a direct impact on the total cost of ownership (TCO) of parts incurred by the OEM. Potential advantages of using multiple suppliers include (Pochard 2003): ? Creates the ability for OEMs to negotiate lower procurement prices during the supplier selection process ? Makes the OEM less susceptible to supply chain risk since OEMs may choose alternative suppliers in the event that the primary supplier is unable to deliver suitable parts ? Allows the OEM to be more selective with part characteristics, such as reliability, quality, and design specifications making the part/supplier selection process more efficient Parts or components are more often purchased from outside sources either directly from component manufacturers (also called ?suppliers?) or through qualified third-party vendors. An important aspect of maintaining an appropriate set of parts begins with selecting an appropriate set of manufacturers or distributors from which to purchase the part. Like any customer in the component market, a product manufacturer must make smart and informed decisions when selecting a reliable component supplier. Manufacturers are assessed by criteria indicative of their reliability and performance in process control, corrective and preventative actions, part traceability, change notification procedures, handling, storage, and shipping 10 (Pecht 2004). The selection process involves qualifying suppliers, regular quality inspections, updating supplier information in databases, and part design verification and testing. A manufacturer selection process is shown in Figure 1.2. For a particular part, the OEM may choose from a number of ?sourcing strategies?. Sourcing strategies commonly used by electronics OEMs are: (1) Sole sourcing ? parts purchased from a single available supplier due to lack of alternatives Figure 1.2 ? Manufacturer (supplier) assessment process flow (Pecht 2004). 11 (2) Single sourcing ? selection of a single supplier from many alternatives by a ?winner-take-all? auction (3) Dual sourcing ? selection of a primary and secondary supplier by a ?split- award? auction (4) Second sourcing ? the option to utilize a licensed back-up supplier or second source should the primary supplier fail (5) Multi sourcing ? use of multiple suppliers simultaneously or as a combination of one or more sourcing strategies shown above (6) Parallel sourcing ? identical (or very similar) parts are procured from multiple suppliers where parts from each supplier are used in a specific product rather than being picked for use from a pool of common parts The remainder of this section provides an overview of the various sourcing strategies employed by procurement management groups and the methods used to assess and select the ideal set of suppliers. It should be noted that a large body of literature exists on sourcing strategies and, although some terms are widely generalized, it is not uncommon for definitions to differ slightly based on the market structure. Sole Sourcing Sole sourcing is rarely employed as a definitive sourcing strategy but is imposed by the state of the market instead. Sole sourcing may be necessary early in the part?s life cycle or as the part approaches obsolescence. For some ?state-of-the- art? technologies, the required part may only be available from one specialized manufacturer. A change in the supply chain structure may occur in order to use 12 additional suppliers when and if they emerge. Sole sourcing may also be observed following the use of other sourcing strategies as a customer may revert to sole sourcing to utilize the last remaining supplier in the market. Single Sourcing In ?single sourcing? a buyer (OEM organization) selects a single exclusive supplier for a particular part. A single sourcing strategy is only possibly when more than one supplier exists in the market, a situation that is common as a part begins to mature and prior to a part phasing-out of the market place. The part and supplier selection is usually a result of a ?winner-take-all? (WTA) auction. A winner-take-all auction is a procurement process that involves selecting and awarding a contract to a winning supplier based on purchase price bids for a specific part. Single sourcing promotes strong customer-buyer relationships by providing opportunities for both parties (supplier and customer) to streamline procurement practices, reduce lead times, and reduce inventory (Larson and Kulchitsky 1998). The customer-supplier relationship also allows part and product decisions to be coordinated. An added benefit of single sourcing is reduced prices for large quantity purchases as a result of ?economy of scale? (Yu et al. 2008). Although single sourcing puts the buyer at risk due to the probability of supply chain disruptions or failures, there may be sufficient confidence in the supplier?s ability to warrant its use. Single sourcing is often used when tooling costs are high and only one supplier is willing to commit to fabricating a particular part. 13 Second Sourcing Second sourcing is a sourcing strategy that involves purchasing parts from a primary supplier while maintaining a qualified back-up supplier (or second source) in the event of a supply chain failure (Anton and Yao 1987). In second sourcing, replacing and incumbent primary supplier by transitioning to a second source (when required) is generally quicker than adopting a new alternative supplier should the primary supplier fail to meet demand. Second sourcing promotes competition at bidding stages offering potentially lower part procurement prices (Anton and Yao 1990). Second sourcing does not compromise ?economy of scale? since all of the required supply is procured from the primary supplier; however, the second source must be maintained on a regular basis to ensure that the supplier?s status is up-to-date, which leads to added costs not incurred by single sourcing. Dual Sourcing Dual sourcing is a sourcing strategy that involves qualifying and purchasing parts from two suppliers simultaneously. The primary contract accounts for a majority of the required parts and is intended to maximize ?economy of scale? while the secondary contract is expected to be more flexible to account for demand uncertainty. From a strategic perspective, a secondary supplier offers supply redundancy should the primary supplier fail to meet the OEMs demand for parts. A dual sourcing strategy utilizes a ?split-award? auction to determine the most cost effective suppliers to use from a procurement cost perspective (Perry and S?kovics 2003). The principles surrounding split-award auctions are that profit 14 incentives are awarded to suppliers with lower price bids. In return, those suppliers are awarded larger volumes to compensate for lost profit. Bidding ensues with each supplier strategically quoting a price high enough to maximize profit but low enough to secure a contract. The total volume required is divided between the winning supplier and the runner-up supplier. The larger volume is awarded to the supplier with the lowest price bid and is the primary contract. The secondary contract is awarded to the runner-up or second-lowest price bid in the split award auction. Like second sourcing, dual sourcing has been found to reduce procurement cost by promoting competition between suppliers in cases where tacit collusion is unlikely (Anton and Yao 1990). Crocker and Reynolds (1993) performed an empirical study on Air Force engine procurement contracts that suggests dual sourcing used in early stages of development reduces the chance of supplier opportunism since procurement contracts tend to be less complete. A customer may also find dual sourcing attractive when innovation is a key dimension in promoting R&D competition (Anton and Yao 1992). However, these benefits of dual sourcing have been debated by Laffont and Tirole (1993), Riordan and Sappington (1989), and Rogerson (1989) who argue that reducing suppliers? production rents affects incentives for R&D (Lyon 2006). Multi-Sourcing Multi-sourcing is a part sourcing strategy that utilizes more than two suppliers from which parts are simultaneously purchased. The volume of parts purchased from each supplier may be allocated evenly or hierarchically based on the supplier?s standing with the OEM. 15 The use of multiple suppliers may involve a combination of attributes from all other sourcing strategies. Companies implement various multi-sourcing strategies to prepare for imminent and unpredictable events. To counteract the likelihood of supply chain disruptions, many organizations prefer ?multi-sourcing? as a way to distribute part purchases among more than two suppliers should one or more suppliers fail to meet required purchase volumes (Burke et al. 2007). A large body of research, related to procurement organizations, addresses the benefits of multi-sourcing as promoting competitive prices as a result of pricing negotiations (Lyon 2006, Anton and Yao 1990). These studies are extensions of (or share attributes with) dual sourcing auction theory. Parallel Sourcing Parallel sourcing involves segregating the purchase of parts between multiple suppliers where parts from each supplier are used in unique products. Therefore, parallel sourcing offers the benefits of multi-sourcing (lower procurement cost from competitive pricing and contract auctions) while allowing commonality across product designs. Parallel sourcing resembles single sourcing in all aspects except that the part from a supplier is limited to a single product. This strategy limits the consequences associated with a specific supplier-related supply chain disruption but may still be susceptible to common mode supplier failures or disasters. 1.1.3 Electronic part management organizations Few of the OEMs that make complex electronic end-products fabricate the individual electronic parts themselves leaving the majority of the electronic systems? 16 hardware content, consisting of ?chips? and other active and passive electronic components, to be procured from elsewhere. A life cycle approach to managing parts within an OEM involves monitoring part characteristics from when a part is first introduced until phase-out. Large OEMs such as Ericsson and Honeywell, have dedicated part selection and management groups whose primary focus is identifying, selecting, qualifying, and purchasing parts for specific products, as well as qualifying the manufacturers and distributors of those parts. The tasks of these groups range from part adoption to obsolescence management and include numerous assembly and support activities that are performed on a regular basis such as determining the procurement status of parts, managing purchase orders, and part database maintenance. In addition, part-specific concerns such as reliability issues and long-term availability problems are the responsibility of these groups if and when they occur. Each part that exists as a unique part number in an organization?s database requires support activities and dedicated resources, which incur life cycle costs that can, in many cases, be significantly higher than the part?s procurement price. To complicate the role of the part selection and management group, actual product manufacturing may be performed by other organizations (e.g., contract manufacturers) that may be outside the control or influence of the part selection and management groups. 1.1.4 Long life cycle vs. short life cycle products Products can be categorized as follows based on the length of the product?s manufacturing and support life cycle: 17 (1) Short life cycle products ? products (often high-volume products) that are manufactured, fielded and supported for relatively short periods of time (1-3 years or less) and therefore only require that a part be available for a relatively short period of time. Examples include consumer electronics: cell phones, personal computers, iPods, televisions, DVD players, etc. (2) Long life cycle products ? products manufactured, fielded and supported for long periods of time (10 years or more ? many are supported for 20-30 years or longer). These products often require relatively low volumes of parts and include: airplanes, medical systems, power plant control systems, infrastructure systems and military systems. Distinguishing between these categories of products is important since they do not share common life cycle characteristics. Existing methods and studies related to managing short life cycle products (and their parts) may not be applicable to long life cycle systems. The distinction between long life cycle and short life cycle products is, in part, due to the nature of the supply chain. Unlike many non-electronic parts, electronic parts are generally not custom produced for customers. Electronic OEMs utilize commercial ?off-the-shelf? (COTS) parts which quickly become obsolete. Therefore it is not uncommon for electronic parts and their supply chains to change outside the control of all but the largest customers. Long life cycle products that generally deal with low volume production have virtually no control over a particular market segment further reducing their ability to interact with suppliers and guide market trends. 18 Long life cycle electronic system using COTS parts in low volumes are subject to the same supply chain constraints imposed by a market that is oriented towards short life cycle, high-volume products. The mismatch between short life cycle parts in long life cycle products increases the likelihood that parts will become unavailable with little or no forewarning. As a result, electronic parts are subject to high-frequency involuntary procurement obsolescence. Many electronic parts are only procurable from their original manufacturer for a few years, then they are discontinued in favor of newer, higher performing parts ? approximately 3% of the global pool of electronic parts become obsolete every month (QTEC 2006). When parts become obsolete, considerable resources must be expended to resolve the problem. 1.1.5 DMSMS type part obsolescence Obsolescence is defined as the loss or impending loss of original manufacturers (suppliers) of items or raw materials (Sandborn 2008b). The type of obsolescence addressed in this dissertation is referred to as DMSMS (Diminishing Manufacturing Sources and Material Shortages) and is caused by the unavailability of technologies (parts) that are needed to manufacture or sustain a product3. DMSMS means that due to the length of the system?s manufacturing and support life, coupled with unforeseen life extensions to support the system, needed parts become unavailable (or at least unavailable from their original manufacturer). Obsolescence 3 Inventory or sudden obsolescence, which is more prevalent in the operations research literature, refers to the opposite problem to DMSMS obsolescence in which inventories of parts become obsolete because the product or system they were purchased for changes so that the inventories are no longer required, e.g., (Brown et al. 1964). 19 is one of many part supply chain problems that complicate the management of electronic systems (Murray et al. 2002). The fundamental disparities in life cycle needs and business objectives impose inevitable obsolescence challenges. Many long field life products particularly suffer the consequences of electronic part obsolescence because they have no control over their electronic part supply chain due to their relatively low production volumes. DMSMS type obsolescence occurs when long field life systems must depend on a supply chain that is organized to support high-volume products. Obsolescence becomes a problem when it is forced upon an organization; in response, that organization may have to involuntarily make changes to products that it manufactures, supports or uses4. Figure 1.3 shows the magnitude of the 4 Researchers who study product-development characterize different industries using the term ?clockspeed,? which is a measure of the dynamic nature of an industry (Fine 1998). The type of 0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 1,400,000 1,600,000 2006 2007 2008 2009 Pr o du ct D is co n tin u an ce N o tic es Figure 1.3 ? The total number of discontinuance notices (notices from the original manufacturer that manufacturing of the part will be terminated) for electronic parts in years 2006-2009 from SiliconExpert Technologies, Inc. databases. 20 obsolescence problem today. The 1.1 million electronic part discontinuances in 2009 represents approximately 0.9% of the electronic parts available in the market.5 The majority of DMSMS obsolescence management today is reactive in nature ? managing problems after they occur using a mixture of the mitigation approaches that include (Stogdill 1999): lifetime buy, last-time buy, aftermarket sources, identification of alternative or substitute parts, emulated parts, salvaged parts, and thermal uprating (Pecht and Humphrey 2006). Potentially larger cost avoidances are possible with pro-active and strategic management approaches (Sandborn 2008b). Pro-active management means identifying and prioritizing selected non-obsolete parts that are at risk of obsolescence and identifying resolutions for them before they are discontinued. Design refreshes ultimately occur as other mitigation options are exhausted and functionality upgrades (technology insertion) becomes necessary. Strategic management is done in addition to pro-active and reactive management, and involves the determination of the optimum mix of mitigation approaches and design refreshes (Singh and Sandborn 2006). industries that generally deal with DMSMS problems would be characterized as slow clockspeed industries. In addition, because of the expensive nature of the products (e.g., airplanes, ships, etc.) the customers cannot afford to replace these products with newer versions very often (i.e., slow clockspeed customers). DMSMS type obsolescence occurs when slow clockspeed industries must depend on a supply chain that is organized to support fast clockspeed industries. 5 As of June 2010 SiliconExpert Technologies? parts database consisted of 157.2 million unique parts (approximately 120 million of which are not obsolete). Part count includes all derivations of part numbers based on part family name and generic codes as assigned by their manufacturers. 21 Chapter 2: Dissertation scope and problem statement This chapter presents the objective, scope, and an overview of the solution strategy followed in this dissertation. 2.1 Problem Statement The goal of this dissertation is to quantify supply chain risk and thereby enable supplier-selection under specific types of sourcing strategies (e.g., single, second, multi-sourcing) subject to long-term supply chain disruptions. 2.1.1 Dissertation Scope This dissertation develops and demonstrates a methodology to quantify the risk of sourcing electronic parts that can be procured from multiple suppliers for use in long life cycle electronic products and systems. This dissertation focuses on part sourcing strategies and decisions (i.e., the number of suppliers and combination of suppliers from which to procure a part) subject to long-term supply chain disruptions, specifically part obsolescence. The comparison of various sourcing strategies for use in the support of long life cycle systems provides application-specific insight into the cost benefits of each strategy as a proactive approach to mitigate the effects of supply chain disruptions. An effect of utilizing multiple suppliers or a specific combination of suppliers, which defines the characteristics of a particular sourcing strategy, is the potential to reduce the overall supply chain disruption risk; however, the benefit may be negated by the cost to qualify and support additional suppliers. The goal of this dissertation is 22 to develop a new methodology that can identify the most ?cost-effective? sourcing strategy to adopt in the procurement and support of particular parts. The quantification and comparison of various strategies involves the assessment of the supply chain risk that a sourcing strategy is exposed to over the part?s usage life cycle (the period of time that the part is used and supported within an organization). Risk is a combination of the following two features: 1) the consequence or severity of a risk related event, and 2) the likelihood that the event will occur. The scope of this dissertation is: ? Part-specific ? The type of supply chain constraints focused on in this dissertation are part-specific, not product-specific since the supply chain constraints considered (e.g., specifications, attributes, available suppliers, etc.) are part specific. In this dissertation product-specific data must be included (e.g., manufacturing volumes as a function of time, end of product support, etc.) and can be allocated on the part level. This approach is suited for the non-product-specific part selection and management groups that exist within large electronic systems OEMs. ? Long life cycle electronic products and systems ? Existing supply chain risk and disruption studies rarely distinguish between long life cycle and short life cycle products and nearly all fall within the realm of short life cycle, high volume production with limited (or unknown) applicability to long life cycle, low volume production. This dissertation focuses on long life cycle (10+ years and often 20-30 year manufacturing and support life), low volume electronic products and systems. ? Strategic parts management ? The focus of this dissertation is on strategic approaches to the mitigation of long-term supply chain disruptions. Tactical 23 solutions for solving short-term problems (e.g., brief lead time problems for delivery of parts to a high-volume manufacturing process) are not addressed within this dissertation. The problems addressed here are disruptions that cause permanent or long term shortages of parts and represent the complex decision making process within part selection and management groups that involve transactions and interactions with suppliers. ? Life cycle approach ? The life cycle of a part selection decision and usage starts when the part is proposed for use in one or more products and ends when the last product that uses the part reaches its end of support. The planning horizon considered for most part procurement decisions ends when manufacturing is complete (and this is the end of the planning horizon considered in the majority of existing sourcing models). Many of the long field life systems that this dissertation is interested in are referred to as ?sustainment dominated,? i.e., their long term sustainment costs are considerably larger than their procurement costs (Sandborn and Myers 2008). As a result, for long life cycle, low volume product sectors, the life cycle cost of a part (the total cost of ownership of the part selection decision) may be significantly higher than the part?s procurement price. ? DMSMS type obsolescence risk ? Although the methodology developed has general applicability to various long term supply chain risks, this dissertation will focus on obsolescence risk in supply chains and present methods of estimating the probability or likelihood of DMSMS type obsolescence occurrence over time. The comparison and selection of sourcing strategies will be assessed based on the likelihood and consequence of part obsolescence. 24 2.1.2 Research overview The goal of this dissertation is to develop and demonstrate a method to quantify supply chain risk (as expected TCO) over the part?s entire support life cycle within an organization (j years) for a particular combination of available sources6 or suppliers. The quantification of supply chain risk enables the selection of suppliers from which to procure parts when the number of suppliers that can be used, SUPSN , is predetermined. In addition, this solution provides a means to perform tradeoff analyses and identify the conditions under which a set of sourcing strategies with SUP SN suppliers will be cost-effective based on the organization?s capability to stream-line qualification and support activities. Let S be the entire set of possible combinations7 of SUPSN sources or suppliers from a set of available/potential suppliers, n. Then, the number of combinations in set S can be calculated using the binomial coefficient in (2.1), )!(! ! SUP S SUP S SUP S NnN n N n S ? =??? ? ??? ? = (2.1) where, SUPSN is the number (integer) of suppliers that can be used in a particular type of sourcing strategy (i.e., single, second, multi sourcing). Each combination of suppliers constitutes a unique sourcing strategy, s where Ss ? . 6 Terms ?sources? and ?suppliers? are used synonymously in this dissertation. 7 Sourcing combinations are assumed to be ?non-repetitive,? e.g., there can be only one combination of two suppliers. In other words, the combination of suppliers is assumed in this dissertation to be independent of order where a sourcing strategy with multiple suppliers shows no supplier preference. Permutations are used instead of combinations in situations where a sourcing strategy defines an order of supplier preference (e.g., ?split-award? auctions - selection of primary and secondary suppliers has an effect on procurement cost through competitive pricing). This dissertation assumes (and later verifies) that advantages gained through reducing part price (as is the goal with competitive pricing) are negligible with respect to part Total Cost of Ownership (TCO) of low-volume long support life products and thus, no supplier preference is assumed. 25 No models currently exist that allow part management organizations to assess long life cycle part management decisions (such as part sourcing), let alone optimize them. The simulation part total cost of ownership (TCO) model developed in this dissertation (presented in Chapter 3) quantifies part TCO, i.e., the total cost of qualifying, procuring, holding, assembling, and supporting parts in multiple products in the presence of supply chain disruptions. Utilizing the new part TCO model, the consequence of supply chain disruptions can be quantified by accounting for the cost of implementing a sourcing strategy, s and effect of the disruption date occurring in year D. The simulation part TCO model was also used to determine when procurement price should (or should not) be considered in the part and supplier selection process. This dissertation presents procurement life as a part-specific and supplier- specific attribute for dealing with the procurement of parts from multiple suppliers. Note that the distribution of D depends upon the sourcing strategy, s. Forecasting the distribution of D with respect to sourcing strategy s is the topic of discussion in Chapter 4. In Chapter 4, a data-driven method is presented to determine the likelihood of part obsolescence. The data-driven method for forecasting a part?s procurement life is especially useful for parts with no identifiable parametric driver for obsolescence. The method utilizes historic part obsolescence data to forecast future obsolescence events via Maximum Likelihood Estimation (MLE). This new method offers a way to determine the likelihood of obsolescence as probability density functions (PDF) and cumulative density functions (CDF). 26 In Chapter 5, the part TCO of introducing and supporting a group of suppliers (from Chapter 3) is combined with the likelihood of disruption (from the data-driven method described in Chapter 4) to quantify the supply chain risk of a part sourcing strategy, s. Letting ( )[ ]DsCE TCO , be the supply chain risk as expected TCO over the part?s life cycle, the problem addressed in this dissertation can be stated as follows: ( )[ ] Ps DsCE minimize TCO ? , Specifically, this dissertation solves the problem described above for obsolescence risk utilizing distributions for supplier-specific procurement life; however, other causes for supply chain disruptions (other risks) could be modeled similarly. The procurement life approach used to quantify supply chain risk offers a clear method in selecting the best single source and best combination of sources when second sourcing. The obsolescence risk results in this dissertation indicate that second sourcing is almost never viable if the cost to support the second source is the same as the first source within the scope of the systems considered in this dissertation. The maximum allowable cost and resources to support a second source in order for a second sourcing strategy to be viable can be calculated mathematically. Chapter 6 derives an analytical part TCO model to estimate the life cycle cost impact of long-term part sourcing based on simplifying assumptions specific to part sourcing in long life cycle electronic products and systems. Section 6.2 derives equations to determine the overlap in supplier-related support activities (via learning indices) that would be needed for the TCO of two sourcing strategies (single sourcing vs. second sourcing) to be equal or ?break-even?. 27 Let aD and bD be the part obsolescence dates (estimated from effective procurement lives) associated with the two sourcing strategies, a and b, being considered. Let Bs be the learning index of support activities for sourcing strategy s. Then, [ ] baTCOC ,? is the difference in CTCO between sourcing strategies, a and b, as shown in (2.2), [ ] ( )[ ] ( )[ ]bSUPbbbTCOaSUPaaaTCObaTCO NBDCNBDCC ,,,,, ?=? (2.2) In the context of this dissertation, learning indices for multi-sourcing support cost are said to be at ?break-even? when the resulting TCO of the two sourcing strategies being compared, strategy a and strategy b, are equal; i.e., ?CTCO becomes zero. The objective of Chapter 6 is to solve [ ] 0? = a,bTCOC for ?break-even? learning index Bb where strategies a and b are single sourcing ( SUPaN = 1) and second sourcing ( SUPbN = 2) strategies respectively. Determining the break-even learning index creates a target for reducing qualification and support activities; a part management organization capable of achieving a learning index below Bb can be expected to benefit from implementing multi-sourcing strategy, b. The analysis includes Monte Carlo simulations based on uncertainties in sourcing-related disruption dates to determine the probability that the ?break-even? learning index will exceed a threshold learning index (or minimum achievable learning index imposed on the part support process). This method is demonstrated in example case studies of linear regulators with a focus on the comparison of single and second sourcing. 28 2.2 Technical tasks In order to meet the objectives described above, the following specific tasks have been completed: Task 1. Construct a Part TCO Model that includes Multi Sourcing Extensions ? Built a general TCO (life cycle cost) model for parts procured from multiple suppliers to enable part sourcing tradeoffs. The total cost of ownership approach captures costs incurred by parts at all stages of their procurement and support life cycle within an organization. The total cost of ownership approach is composed of part-related non-recurring design and selection/qualification activities, product manufacturing and assembly activities, product field support activities, and regular support activities critical to the management of electronic parts in long life cycle products. Include the effects of long-term supply chain disruptions into the TCO simulator. The cost (inclusive of disruption effects and penalties) is estimated as a function of disruption year. Task 2. Obsolescence Risk Model Formulation ? Formulate a methodology to estimate the probability (likelihood) of occurrence of a long-term supply chain disruption. The dissertation focuses on the particular risk of DMSMS type part obsolescence and uses historic part obsolescence data to formulate a model. Include the obsolescence risk likelihoods (probability distributions of disruption events) within the simplified TCO model to estimate the ?expected TCO? of a sourcing strategy. This allows sourcing strategies to be compared based on obsolescence driven supply chain risk. 29 Task 3. Case Studies with Part TCO Simulator (determination of viable assumptions for the analytical model developed in Task 4) ? Implement the part TCO model as a simulation to assess the life cycle cost of managing electronic parts. Surface mount capacitor case studies are used to establish the applicability of simplifying assumptions for long-term sourcing in long life cycle products. Task 4. Analytical TCO Model ? Derive an analytical part TCO model based on simplifying assumptions specific to the long-term sourcing of parts used in long life cycle products and systems (gathered from Task 3). Formulate a method to asses sourcing tradeoffs such as estimating the benefit (or cost) of extending the procurement life of a part by adding suppliers. Tradeoff analyses between part sourcing strategies help to make ?evidence based? decisions by estimating the cost and risk tradeoffs between two sourcing strategies (for example, single versus second sourcing). The tradeoff analyses includes mathematically estimating learning indices for sourcing support costs that would be required for the TCO of two sourcing strategies (with different procurement lives) to be equal or ?break-even?. Task 5. Determine the Viability of Second Sourcing Compared to Single Sourcing Parts ? Viability of the second sourcing strategy is dependent on the probability that the ?break-even? learning index will exceed a threshold learning index. 30 Chapter 3: Part sourcing total cost of ownership (TCO) The model presented in this chapter focuses on optimal part management from a part selection and management organization?s viewpoint as opposed to the optimum part management from a product group?s perspective. These perspectives differ because the part selection and management group has a more holistic view of a part?s cost of ownership than a product group, and a part (especially an electronic part) may be concurrently used in many different products within the same organization. This approach requires a cost model that comprehends long-term supply chain constraints that are associated with specific parts and their effects downstream at the product level, therefore the cost that we wish to predict and minimize is the effective total cost of ownership (TCO) of the part as used across multiple products. Assessing the total cost incurred over the life cycle of the part as an effective total cost of ownership will allow part management organization to quantify the cost spent (inclusive of procurement) per part for a specific sourcing configuration. In Section 3.3, the part TCO model (described in Section 3.1) is applied in a general way to enable the estimation of part life cycle cost under various conditions of use representative of long life cycle product applications. Section 3.3.1 describes example case studies of an SMT capacitor to demonstrate the evaluation of part TCO. These example case studies will present the basis for key assumptions made in the formulation of an analytical part TCO model for parts used in long life cycle products in Chapter 6. 31 3.1 Part TCO model for single sourcing The part TCO model discussed in this section estimates the total cost of introducing, procuring, storing, assembling, and supporting a part from a single supplier in multiple products. Let j be the part lifetime (the number of years in which the part will be used). Then, the part TCO, ( )DsCTCO , after j years, if the product manufacturer chooses sourcing strategy s and a disruption occurs in year D, is the total cost spent at various stages of the part?s life cycle: procurement (CPROC), inventory (CINV), support (CSUP), assembly (CASY), and field failure repairs (CFF). The part TCO can be calculated as shown in (3.1), ( ) ( ) ( ) ( ) FFASYSUPINVPROCTCO CCDsCDCDsCDsC ++++= ,,, (3.1) Modeling a part?s total cost of ownership requires an understanding of the product?s life cycle costs8. Life cycle cost represents the total cost of acquisition and ownership of a product over its full life, including the cost of planning, development, acquisition, operation, support, and disposal. General life cycle cost analyses of products have been treated by many authors, e.g., (Fabrycky and Blanchard 1991, Asiedu and Gu 1998). Existing models used to estimate part management cost tradeoffs tend to be either: a) primarily focused on manufacturing (containing little or no view into the post-manufacturing life cycle), b) product specific, and/or c) lack an understanding of the unique attributes of electronic part management. For example, the methodology presented by Boothroyd and Dewhurst (1994) presents an assembly (DFA) and manufacturing (DFM) approach to product cost modeling that does not 8 In this chapter the effective total cost of ownership refers to the life cycle cost of the part from the part customer?s point of view, which should not be confused with Cost of Ownership (COO), which is a manufacturing cost modeling methodology that focuses on the fraction of the lifetime cost of a facility consumed by an instance of a product. 32 capture activities beyond the manufacturing of the system. In another example, Wang et al. (2007) establishes a decision-support model in order to enable part changes from a life cycle cost perspective, however, the cost model estimates static and dynamic costs from a product perspective as opposed to a part perspective. Ellram and Siferd (1998) describe the common shortcomings of traditional cost analysis methods as being focused on price, de-emphasizing suppliers? performance, and disregarding internal costs. In addition, traditional cost analysis methods often tend to focus on aspects of an organization that lack efficiency rather than modeling all processes. Ellram and Siferd support the emergence of total cost of ownership (TCO) approaches to promote strategic decision making and that the true benefits of total cost of ownership is the marriage between strategic cost management concepts (focus on financial and accounting perspectives) and the fundamental approach of total cost of ownership as a holistic costing approach ? concepts that are captured in the model presented in this section. The estimation of life cycle cost in electronic parts (besides procurement) include the assessment of part manufacturers and distributors (Jackson et al. 1999), qualifying and screening parts (e.g., Kim 1998), the impacts of part reliability (e.g., Alcoe et al. 2003), warranty, sparing and availability, obsolescence management (Sandborn 2008a), and support. The proposed part total cost of ownership (TCO) model is composed of the following three sub- models: part support model, assembly model, and field failure model. This TCO model contains both assembly costs (including procurement) and life cycle costs associated with using and supporting the part in multiple products. 33 From a traditional part management perspective, the term ?part? is used to describe one or more items with a common part number. Several items with a common part number may be used in multiple products as an artifact of design reuse (Meyer and Lehnerd 1997). A ?part site? is defined as the location of a single instance of a part in a single instance of a product. For example, if the product uses two instances of a particular part (two part sites), and 1 million instances of the product are manufactured, then a total of 2 million part sites for the particular part exist. In this dissertation, we focus on the ?part sites? (instead of ?parts?) because when product repairs and replacements are considered there is effectively more than one part consumed per part site (e.g., if the original part fails and is replaced, then two or more parts occupy the part site during the part site's life). For consistency, all cost calculations are presented in terms of either annual or total (cumulative) cost per part site. Let VOLiN be the number of parts used (consumed by assembly operations) in year i. Then CPPS is the total effective cost (TCO) per part site as shown in (3.2). ?? == ++++ == j i VOL i FFASYSUPINVPROC j i VOL i TCO PPS N CCCCC N C C 11 (3.2) All computed costs in the model are indexed to year 1 (base year for money) for reference where year 1 refers to the period between time 0 and the end of 1 year. 34 3.1.1 Support cost model The part support model captures all costs associated with selecting, qualifying, purchasing, and sustaining a part (these costs may recur annually, but do not recur for each part instance). Let x be a vector of support activities where xiC are cost components of the total support cost incurred during year i. For example, iaiC , pa iC , as iC , ps iC , and so on, are costs attributed to the management of electronic parts determined from an activity based cost model in which cost activity rates can be calculated by part type.9 These support activities can be described as follows (and shown in Table 3.1): ? Recurring Costs ? incurred on several occasions, often at fixed time intervals (e.g., annual costs). Conversely, Non-recurring costs are incurred once (e.g., product qualification). 9 Part type definitions are as follows: Type 1 ? resistors, capacitors, inductors, and mechanical parts; Type 2 ? integrated circuits, oscillators, filters, board connectors; Type 3 ? ASICs, RF connectors, RF integrated circuits, DC/DC, synthesizers, optical transceivers (TRX); and Type 4 ? RF transistors, circulators, isolators. Table 3.1 ? Example matrix of the characteristics of various support activities, x. Support activities (x) Recurring Fixed Initial Approval No Yes Part NRE Cost No No Product-Specific Approval Yes No Supplier Qualification No Yes Annual Part Data Management Yes No Annual Production Support Yes Yes Annual Purchasing Yes No Obsolescence Case Resolution No No 35 ? Fixed Costs ? not dependent on a specific independent variable and therefore, do not vary (e.g., initial approval). Conversely, Variable costs are driven by one or more independent variables (e.g., product specific approval costs are dependent on the number of products that the part is used in, Nsup). Let iaiC be the initial part approval and adoption cost. The approval cost is assumed to occur only in year 1 (i = 1) for each new part. iaiC includes all costs associated with qualifying and approving a part for use (i.e., setting up the initial part approval). This could include reliability and quality analyses, supplier qualification, database registration, added NRE for part approval, etc. Let paiC be the product-specific approval and adoption cost. pa iC includes all costs associated with qualifying and approving a part for use in a particular product. This approval cost would occur exactly one time for each product that the part is used in and is a function of the type of part and the current approval level of the part within the organization when the part is selected. This cost depends on the number of products introduced in year i that use the part. Let asiC be the annual cost of supporting the part within the organization. as iC includes all costs associated with part support activities that occur for every year that the part must be maintained in the organization's part database such as database management, PCN (product change notice) management, reclassification of parts, and services provided to the product sustainment organization. asiC depends on the part?s qualification level which can change over time. 36 Let psiC be the total cost associated with production support and part management activities that occur every year that the part is in a product manufacturing (assembly) process. asiC includes all costs associated with volume purchase agreements, services provided to the manufacturing organization, reliability and quality monitoring, and availability (supplier addition or subtraction). Let apiC be the purchase order generation cost which depends on the number of purchase orders in year i. Let oriC be the obsolescence case resolution cost. or iC is only charged in the year that a part becomes obsolete. Let nonPSLiC be the cost to setup all non-PSL (Preferred Supplier List) part suppliers. nonPSLiC depends on the number of non-PSL sources that must be qualified in year i. Let designiC be the non-recurring design-in costs associated with the part. design iC is only charged in years when new products are introduced and includes cost of new CAD footprint and symbol generation if needed. Then, the total support cost, SUPC , after j years, can be calculated as shown in (3.3) where j is the number of years that the part must be supported. ( )? = + +++++++ = j i i design i nonPSL i or i ap i ps i as i pa i ia i SUP r)( CCCCCCCCC 1 1 (3.3) 37 3.1.2 Assembly cost model The assembly cost model captures all recurring (for each instance of the part) costs associated with the assembly of the part: system assembly cost (part assembly into the product or system), and recurring functional test/diagnosis/rework costs. Let VOLiN be the total number of parts consumed by assembly operations in year i. Let INpiY be the yield of the assembly process in year i when parts are procured from supplier p. Let aiC be the assembly cost and Pi be the purchase price of one instance of the part in year i. Let INiC be the annual incoming cost (per part) inclusive of part price (i.e., aiiINi CPC += ). Then ASYC be the total assembly cost (for all products and inclusive of procurement cost) after j years, as shown in (3.4), ( )? = + = j i i VOL i IN pi IN i OUT i VOL i ASY r)( NYCCN C 1 1 ,, (3.4) where, OUTiC is the assembly cost (per part) during year i. OUTiC is calculated annually using the assembly cost model shown in Figure 3.1 where OUTiout CC = , IN iin CC = , VOL iin NN = and IN piin YY = . The model described in Figure 3.1 and Table 3.2 is based on a previously developed test/diagnosis/rework model for the assembly process of electronic systems (Trichy et al. 2001).10 The approach includes a model of functional test operations characterized by fault coverage, false positives, and defects introduced during tests, in addition to rework and diagnosis (diagnostic 10 Note, several typographical errors should be corrected in (Trichy et al. 2001): In (2) and (3), the maximum of the summation should be n-1 instead of n, and (4a) can be used for either definition of fp with 1ndN + changed to ndN 1 . In (13), the subscript of Nr should be i-1 instead of i when i > 0. 38 test) operations that have variable success rates and their own defect introduction mechanisms. The model accommodates multiple rework attempts on any given product instance and enables optimization of the fault coverage and rework investment during assembly tradeoff analyses. The model discussed in this chapter contains inputs to the test/diagnosis/rework model that are specific to the part type and how the part is assembled (automatic, semi-automatic, manual, pre-mount, lead finish11, extra visual inspection, special electro static discharge (ESD) handling ? see (Prasad 1997)). The output of the model is the effective procurement and assembly cost per part site. This model assumes that all part-level defects (either inherent in the part or introduced during the assembly process) are resolved in a single rework attempt (i.e., Yrew = 1), that there are no defects introduced by the testing process (i.e., Ybeforetest = Yaftertest = 1), 11 Lead finishes are very relevant for electronic parts since traditional tin-lead solder finishes were banned for many electronic product sectors in 2003 by the RoHS directive (Ganesan and Pecht, 2006). Cin, Yin, Nin Cout, Yout, NoutTest (Ctest , fc , fp ) Defects (Ybeforetest ) Defects (Yaftertest ) R ew o rk ed Repairable (N r ) To be diagnosed (Nd ) Scrap ( Ns1 ) Diagnosis ( fd, Cdiag ) No Fault Found Ngout Nrout Rework (fr, Crew,Yrew) Nd1 Scrap ( Ns2 ) R ew o rk ed Figure 3.1 ? Test/diagnosis/rework (TDR) model from Trichy et al. (2001). Table 3.1 describes the notation appearing in this figure. 39 and that there are no false positives in testing (i.e., fp = 0). These assumptions for yields in the assembly process guarantee that Yout will always be 1. As a result, VOL ioutin NNN == and 021 == ss NN . Therefore, if part price is omitted from the calculation of INiC (i.e., aiINi CC = ), then ASYC is the total assembly cost exclusive of total procurement cost. Section 3.1.3 presents a model for calculating the part?s procurement and inventory cost subject to disruption dates. The calculation of ASYC is independent of disruption date if sufficient parts are procured through lifetime buys when a disruption occurs (also discussed in Section 3.1.3). The cost (and penalties) of other disruption mitigation strategies may be considered and is the topic of discussion in Section 3.2.5. 40 3.1.3 Procurement and inventory cost model The part?s total procurement and inventory costs depend on when part disruptions occur. For every year before the disruption occurs, the manufacturer purchases exactly the number of parts needed for that year. In the year of the Table 3.2 ? Nomenclature used in Figure 3.1. Cin = Cost of a product entering the test, diagnosis and rework process Nin = Number of products entering the test, diagnosis and rework process Ctest = Cost of test per product Nd = Total number of products to be diagnosed Cdiag = Cost of diagnosis per product Ngout = Number of no fault found products Crew = Cost of rework per product Nd1 = Nd ? Ngout Cout = Effective cost of a product exiting the test, diagnosis and rework process Nout = Number of a products exiting the test, diagnosis and rework process, includes good products and test escapes fc = Fault coverage Nr = Number of products to be reworked fp = False positives fraction, the probability of testing a good product as bad Nrout = Number of products actually reworked fd = Fraction of products determined to be reworkable Ns1 = Number of products scrapped by diagnosis process fr = Fraction of products actually reworked Ns2 = Number of products scrapped during rework Ybeforetest = Yield of processes that occur entering the test Yaftertest = Yield of processes that occur exiting the test Yin = Yield of a product entering the test, diagnosis and rework process Yout = Effective yield of a product exiting the test, diagnosis and rework process Yrew = Yield of the rework process 41 disruption, the manufacturer makes a lifetime buy plus an overbuy quantity called a ?buffer,? a purchase of more parts than the demand forecasts. In subsequent years, the cost of procuring parts becomes zero, but the cost of inventory for the lifetime buy of parts is included. Let VOLiN be the number of parts used by assembly operations in year i. Let ( )PROCpiN D be the number of parts purchased from supplier p in year i when the disruption occurs in year D. Note that D can range from 1 to j+1. Let k be the counter variable for each year after the disruption date until year j. Let Foverbuy be the lifetime buy quantity buffer expressed as a fraction of the lifetime buy quantity. Then )(DN Ti is the total number of parts purchased in year i. In the case of a single supplier, )()( DNDN PROCpiTi = . ( ) ??? ??? ? >? =? D. Let ih be the cost of holding one part in year i. Then ( )INVC D is the total inventory cost after j years when the disruption occurs in year D. ( ) ( )( )?= += j i i ii INV r DQh DC 1 1 (3.6) 3.1.4 Field failure cost model The field failure model captures the costs of warranty repair and replacement due to product failures caused by the part. Let failiN be the number of failures under warranty in year i. This is calculated using 0-6, 6-18 and > 18 month FIT rates12 for the part, the warranty period length (an ordinary free replacement warranty is assumed with the assumption that no single product instance fails more than one time during the warranty period), and the number of parts sites that exist during the year. Let Crepair be the cost of repair per product instance for failures under warranty. Let frep be the fraction of failures requiring replacement (as opposed to repair) of the product. Let Creplace be the cost of replacing the product per product instance. Let wriC be the cost of processing the warranty returns in year i. Then, FFC is the total cost of field failures after j years as shown in (3.7). 12 FIT (Failures in time) rate ? Number of part failures in 109 device-hours of operation. 43 ( )? = + ++? = j i i wr i fail ireplace fail irepairrep fail i FF r)( CNf CN CfN C 1 1 1 (3.7) Section 3.3 presents case studies using the TCO model for single sourcing (described in Section 3.1) to explore the true impact of variability in procurement cost on a part?s TCO when used in long life cycle applications. These case studies provide the basis for simplifying assumptions in the formulation of an analytical part TCO model. Section 3.2 modifies the models presented in Section 3.1 to address the cost impact of using multiple part sources. 3.2 Modifications to address multi-sourcing This section describes the formulation of a multi-sourcing part TCO model for electronic parts based on the part TCO model described in Section 3.1. The inclusion of sourcing-related effects enables the life cycle cost impact of sourcing decisions to be quantified. In Section 3.2, the total cost of ownership is determined as a function of the sourcing strategy used, s and the forecasted date of a long-term supply chain disruption, D ? determining the probability and thereby forecasting the risk of supply chain disruptions will be addressed in Chapter 4 and Chapter 5 respectively. The value of multi-sourcing involves modeling the cost benefits of price auctions as well as the added cost needed to support multiple suppliers. In order to accurately assess a sourcing strategy, one must capture all facets of the supplier selection decision and the effects of long-term supply chain problems over the life of the electronic part. Modeling sourcing strategies as a total cost of ownership helps quantify the consequences of long-term supply chain disruptions. 44 The electronic part total cost of ownership model discussed in Section 3.1 computes the effective lifetime cost of a part?s selection based on the part?s properties, the characteristics of the organization using the part, financial costs, the quantity of parts used, and the quantity and mix of products that use the part. An observation from the case studies that will be described in Section 3.3 is that for low- volume parts used in long life cycle products, a significant portion of the total cost of ownership is attributed to assembly and support activities, and specifically the supplier setup component of support cost contributed significantly to a part?s total cost of ownership. The effects of adding a supplier to the procurement plan (transitioning from a single source to a multi-source strategy) would be expected to drive part procurement prices down as a result of competitive pricing, but it will also increase the total support cost since a majority of the support activities will need to be repeated for additional suppliers. Some supplier related costs include: a) initial approval ? supplier qualification, reliability and quality analyses, database registration, etc., b) annual maintenance support ? maintaining a part in an organization?s database, and c) annual production support ? volume purchase agreement work, reliability and quality monitoring, etc. In short, for long life cycle systems, TCO is driven by a number of recurring and non-recurring support costs that are duplicated with the addition of suppliers. In the existing literature related to optimum sourcing, an emphasis is placed on aspects such as procurement cost benefits via auction theory (Anton and Yao 1992, Riordan and Sappington 1989, Laffont and Tirole 1993) under demand uncertainty (Li and Debo 2009) and supplier uncertainty (Gurnani and Ray 2003). 45 The risk of supply chain disruptions, for a particular supply chain structure, has also been addressed as delivery lead times (Gaonkar and Viswanadham 2004) and logistics of the part (Ruiz-Torres and Tyworth 2000), i.e., transportation, inventory, etc. These studies, although important on the operational and tactical level, neither capture long-term disruptions (and their effects) nor consider costs beyond procurement-related processes (negotiation practices, customer-supplier relationships, etc.). The only known existing work addressing sourcing for long-field life systems is from (Lyon 2006). Lyon performs an assessment of three popular sourcing strategies used by the United States Department of Defense (DoD) in the procurement of missiles13 ? sole-sourcing, dual sourcing (?split-award? auction) and single sourcing (?winner-take-all? auction). The assessment involves studying the impact of sourcing strategies on a missiles? ?flyaway cost? (a term used to describe the total cost spent by the U.S. Government on each missile). Lyon uses ?flyaway cost? as a metric to test the applicability of the following hypotheses found in high-volume, short life cycle sourcing literature: Hypothesis 1: Dual sourcing is more likely to be used after the incumbent [supplier] charges a high price. Hypothesis 2: Dual sourcing is more likely to be used after the incumbent producer delivers products with quality defects. 13 Procurement of missiles by the U.S. Department of Defense adheres to procurement regulations related to long-term, high-technology defense programs that require the use of competitive bidding by law (Kratz et al. 1984). 46 Hypothesis 3: Dual sourcing is more likely for technologically complex [systems] without substantial economies of scale or steep learning curves, and in early periods of production. Hypothesis 4: Dual sourcing is likely to be followed by a winner-take- all auction. Lyon concludes that the benefit to dual sourcing is two-fold: 1) dual sourcing reduces information asymmetries in suppliers reducing procurement prices through competitive bidding in subsequent auctions, and 2) dual sourcing gives the buyer more control over non-contractible dimensions of quality. The empirical study by Lyon finds a 20% procurement cost reduction in missile systems that employ a dual sourcing policy. Indeed, technological uncertainty at early stages of production limits the suppliers? ability to coordinate bids in a ?split-award? auction thereby reducing their ability to achieve monopolistic prices. The studies support the prediction that program managers resort to dual sourcing significantly more often when the supplier experiences quality control problems. The empirical results, although not statistically significant at standard levels, indicate additional procurement cost savings to the government when a ?winner-take-all? auction is conducted following periods of dual sourcing. A switch from dual sourcing to a winner-take-all auction (single sourcing) is frequently observed in the data set. Sourcing decisions are made at the discretion of program managers responsible for the procurement of defense systems. Lyon?s study captures the tendency of program managers towards specific sourcing decisions but offers only 47 very limited insight into the true life cycle cost of each sourcing strategy. The primary shortcoming of the Lyon work is the focus on price rather than production cost in developing learning curves. General conclusions based on the data set of missiles cannot be translated to procurement of electronics without the verification of cost contributions from each stage of the life cycle. As established in Section 3.3, the procurement cost of electronic parts is a minute contributor to life cycle cost; so Lyon?s study does little to justify the use of dual sourcing in electronics (from a life cycle perspective) based on the available empirical results. Furthermore, the use of learning curves from a top-down perspective offer some disadvantages. For example, Lyon?s method does little to help in assessing part management decisions since recurring and non-recurring cost components are dealt with as a total cost instead. These recurring and non-recurring costs vary based on the selection of a part or supplier so, in order to utilize them for part management decision making purposes, an understanding of management processes is necessary. The remainder of this section discusses the total cost of ownership model from a part sourcing perspective. 3.2.1 Support cost model Cost changes for additional suppliers can be represented empirically as ?learning curves,? which reflect improvements in management, methods, processes, tooling, and engineering time. Learning curve models have been applied to relate production cost to the number of units produced for various industries such as airframes (Wright 1936), machine tools (Hirsch 1952), automotive (De Jong 1964), construction (Everett and Farghal 1994), chemical processing (Lieberman 1984), 48 software development (Raccoon 1996), and integrated circuits (Dick 1991). Lyon applies learning curves to represent learning effects responsible for inducing collusion in dual sourcing (Lyon 2006). Lieberman (1984) discusses the conditions to reliably use price data for estimating such learning curves. However, the application of learning curves to support activities cannot be found in existing sourcing literature. An implementation of the Crawford or Boeing model (Crawford 1944) for supplier- related support cost is shown in (3.8). In (3.8), learning curves are applied to support activities to maintain the ?bottom-up?14 costing approach. Incorporating learning curves into the total cost of ownership offer a means to capture the decrease in support activity cost when supporting multiple suppliers wherein information gathered on prior attempts reduces the time (or effort) needed for subsequent attempts of the same activity. The following is an extension to the support cost model presented in Section 3.1.1 to address multi-sourcing. Let xiC be the annual contributions to support cost from a support activity x. Let n be the number of support activities in vector x. Then ),,( SUPsxSUP NBDC is the total support cost after j years when a disruption occurs in year D, assuming that the cost of support activities, x (part and product qualification, annual data management, production support, annual purchasing, etc.), are subject to a learning index ( xB ). 14 A ?bottom-up? approach to cost modeling assesses life cycle cost by the accumulation of cost components (Sandborn and Prabhakar 2008). 49 ( )? ? ? = = = + = j i i n x N p Bx i SUP s x SUP r pDC NBDC SUP sxi x i 1 1 1 1 )( ),,( (3.8) In (3.8), if xiB = 0, then no learning occurs and all support activities are completely repeated for each subsequent supplier (e.g., the cost of supporting two suppliers is exactly double the cost of supporting one supplier). If B < 0 then support activities (and thereby, support cost) decreases for subsequent suppliers (e.g., the cost of supporting two suppliers is less than double the cost of supporting one supplier). For example, when B = ??, then the addition of subsequent suppliers requires no support activities and therefore adds no support cost. Similarly, if B > 0 then support cost increases for subsequent suppliers (e.g., the cost of supporting 2 suppliers is more than double the cost of supporting one supplier). The number of suppliers, SUPsN , is dependent on the sourcing strategy used, s. For example, SUPsN =1 for single sourcing and SUP sN = 2 for second sourcing. However, the number of suppliers that actually require a particular support activity may be unique to the type of sourcing strategy and varies annually. In practice, the activities performed for certain sourcing strategies may differ despite using the same number of suppliers. For instance, second sourcing and dual sourcing both use two suppliers. However, when second sourcing, parts are procured from the two suppliers interchangeably. On the other hand, when dual sourcing, parts are procured from both suppliers simultaneously (i.e., purchase orders are separated effectively doubling the resources needed for generating purchase orders). In order to distinguish between two sourcing strategies, an array of SUPsxN is used to define the characteristics of the 50 sourcing strategy to model support cost (where SUPsSUPsx NN ? ). An example matrix of the variable SUPsxN with respect to various support activities, x is shown in Table 3.3. 3.2.2 Assembly cost model The assembly cost is dependent on the effective incoming yield of purchased parts as discussed in Section 3.1.2. The quality of parts for each batch received is dependent on their supplier?s manufacturing and quality control process. Therefore, the incoming yield of parts changes based on supplier selection. Let SUPsiN be the number of suppliers from which parts are purchased in year i when sourcing strategy s is used. Let ?pi be the fraction of total part usage that is purchased from supplier p. Let Yp be the yield of parts purchased from supplier p. Then INsiY is the effective incoming yield of parts entering the assembly process (from multiple suppliers) during year i. Table 3.3 ? Example matrix for the number of suppliers ( SUPsxN ) for which support cost components (x) are applicable with respect to various sourcing strategies. Number of suppliers ( SUPsxN ) Support cost components (x) Single Second Dual Initial Approval 1 2 2 Part NRE Cost 1 2 2 Product-Specific Approval 1 2 2 Supplier Qualification 1 2 2 Annual Part Data Management 1 2 2 Annual Production Support 1 1 2 Annual Purchasing 1 1 2 Obsolescence Case Resolution 1 1 2 51 ? = = SUP siN p ppi IN si Y?Y 1 (3.9) ? = == SUP siN p pii ?? 1 1 (3.10) For example, consider the case where a part is procured from two suppliers with indices, p = 1 and p = 2, and corresponding yields, Y1 and Y2. The fractions of the total part usage volume procured from each supplier are ?1 and ?2 respectively. Let GpVol be the number of good parts from supplier p before the assembly process begins i.e., parts free from defects. Let ( )DN PROCpi be the volume of parts procured from supplier p in year i when the disruption occurs in year D. Let TiN be the total number of parts procured for assembly in year i. Then, the effective incoming yield for parts procured from the two suppliers for a particular year is, ( ) ( ) T PROCPROC T GG IN N DNYDNY N VolVolY 221121 +=+= 2211 YYY IN ?? += where, Tpp VolVol? /= The model in Section 3.1.2 assumes that the effective yield of incoming parts is known and remains constant over the entire simulation period. However, using (3.9), the effective incoming yield can be estimated from supplier-specific yield values. The multi-sourcing assembly model assumes that parts from each supplier can be treated as identical within the assembly process and incur the same assembly- related costs. 52 3.2.3 Procurement and inventory cost model Part price may vary from one supplier to the next and so the procurement cost (exclusive of inventory) incurred after j years for a part varies based on the volume purchased from each supplier. This procurement and inventory cost model for multi- sourcing is based on the model presented in Section 3.1.3. Let p be a supplier that is selected in sourcing strategy s where sp? and s consists of SUPsN suppliers. Let ( )DN PROCpi be the number of parts purchased from supplier p in year i when the disruption occurs in year D (the last year parts are available from any supplier). Note that D can range from 1 to j+1. Assuming that a lifetime buy is made in year D, let overbuyF be the lifetime buy buffer expressed as a fraction of the lifetime buy quantity. We assume that the buffer quantity is apportioned among the available suppliers by ?pi, the fraction of total part usage that is purchased from supplier p in year i, if multiple supplier-specific disruptions occur in year D. Let SUPpiP be the supplier-specific part price in year i (subject to annual cost changes due to inflation or deflation) when supplier p is selected. Let k be the counter variable for each year after the disruption date until year j. Let pi? be the fraction of total part usage, VOLiN that is purchased from supplier p in year i. ( )DN PROCpi can be calculated for sourcing strategy s as follows, 53 ( ) ( ) ? ? ? ? ? ?? ? ? ? ? >? =?+ 0), indicating that the longer the procurement lifetime, the more likely the part is to go obsolete. The analysis described in this section has been applied to a variety of electronic parts; Table 4.1 provides results for selected part types. In the case of the linear regulators, there are 347 obsolescence events out of a total of 847 introduced parts. 18 The MLE parameter estimation was performed using the MatLAB Statistics package. 77 Table 4.1 ? Procurement lifetimes for various electronic part types through 2008. ? and ? refer to 2 parameter Weibull fits of the censored and uncensored PDFs. LKV is the negative log-likelihood function (larger negative values indicate a better fit). Censored Uncensored Part Type Mean (years) ? ? LKV Mean (years) ? ? % of parts not obsolete Total number of parts not obsolete Linear Regulators 11.63 2.84 13.06 -1205 8.25 3.47 9.17 59.46% 509 Buffer & Line Drivers 38.39 2.02 43.33 -3042 9.82 4.01 10.83 91.08% 1279 Bus Transceivers 15.39 2.29 17.37 -1746 9.28 4.99 10.11 57.26% 1057 Decoder & Demux 20.74 1.71 23.25 -914.9 9.30 4.51 10.19 62.30% 565 Flip Flop 16.23 2.25 18.33 -1727 9.64 5.15 10.48 58.27% 1052 Inverter Schmitt Trigger 18.13 1.83 20.40 -1125 8.58 4.06 9.453 64.13% 750 Latch 14.99 2.29 16.92 -1391 9.19 4.95 10.01 55.46% 818 Multiplexer 18.83 1.82 21.19 -844.0 8.84 4.10 9.734 63.70% 552 78 Figure 4.5 shows the quantity and fraction of non-obsolete parts as a function of time. This plot shows that a large fraction of the parts introduced in 1990-1996 have not gone obsolete yet (but the total number introduced during this period is also relatively small). An alternative way to look at this is to perform the analysis described above for determining the mean procurement lifetime on the data set as a function of time (Figure 4.7). In this case, to generate the mean procurement lifetime at a particular date (or before), the parts that had been introduced on or before that date in the analysis are only considered (although all observations are made in 2008). The mean procurement life is analogous to the mean time-to-failure (MTTF). The mean procurement life for a given Weibull distribution can be calculated using, ??? ? ??? ? += ??? t1Lp (4.5) 0 100 200 300 400 500 600 1991 1993 1995 1997 1999 2001 2003 2005 2007 Introduciton Date Nu m be r o f P ar ts th at ar e No t O bs o le te 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Fr ac tio n o f P ar ts th at ar e No t O bs o le te Number of Parts (left axis) Fraction of Parts (right axis) Introduction Date (DI) Figure 4.5 ? Quantity and percentage of linear regulators that are not obsolete as of 2008 as a function of time. 79 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 0 5 10 15 20 25 Year M ea n Pr oc u re m en t L ife (Y ea rs ) Censored - Weibull (2-P) Uncensored - Weibull (2-P) Uncensored - Normal Dist. Introduction Date (DI) M ea n Pr o cu re m en t L ife (L P) in Ye ar s Figure 4.6 ? Mean procurement lifetime for linear regulators as a function of time (parts introduced on or before the date). where ? and ? are the Weibull parameters corresponding to the data fits limited by DI. Figure 4.6 indicates the appropriate mean procurement lifetime to assume for parts with introduction dates at or before the indicated year. So a part introduced in 1998 or before has a mean procurement lifetime of 14 years (Censored ? Weibull (2-P) in Figure 4.6). In order to determine the mean procurement lifetime for part introduced in a particular year (rather than in or before a particular year), ?slices? of the data must be used. In this case, to generate the mean procurement lifetime at a particular date, the parts that have been introduced within one year periods in the analysis are only considered and once again, all observations are made in 2008. Figure 4.7 shows the mean procurement lifetimes for one year slices with and without right censoring assuming that the observation is made in 2008. For a part introduced in 1998, Figure 80 4.7 predicts that the mean procurement lifetime will be 11.5 years (smaller than the 14 years predicted by Figure 4.6). Figure 4.7 and the comparison of Figures 4.6 and 4.7 indicate that older linear regulators (smaller DI) have longer procurement lifetimes (LP) than newer linear regulators. Using the data from Figure 4.7 for 1990-2005 (excluding 1993 since no parts were introduced in 1993), the mean procurement life trend is given by, 86096222.850211.0 2 +?= IIp DDL (4.6) The analysis in this section provides a useful estimation of the mean procurement lifetime for parts, however, the worst case procurement lifetimes are also of interest to organizations performing pro-active and strategic DMSMS obsolescence management. Sandborn et al. (2007) provides a more detailed M ea n Pr o cu re m en t L ife (Y ea rs ) Introduction Date (DI) 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 0 5 10 15 20 25 Censored - Weibull (2-P) Uncensored - Weibull (2-P) Uncensored - Normal Dist. M ea n Pr o cu re m en t L ife (L P) in Ye ar s Figure 4.7 ? Mean procurement lifetime for linear regulators as a function of time (parts introduced on the date). Note, there were no parts introduced in 1993. 81 interpretation of (procurement life versus introduction date profiles) and discusses the generation of worst case forecasts. 4.2 Supplier-specific obsolescence likelihood (MLE) The methodology described in Section 4.1 can also be applied to specific manufacturer data as shown in Section 4.2. The procurement lives (LP) observed for a subset of the historic part data can be fit with a Weibull (2-parameter) using Maximum Likelihood Estimation (MLE) to provide estimates for parameters ? (shape) and ? (scale). The resulting distribution is representative of the uncertainty in procurement life for a subset of parts within a particular part type; in this case, the data and results are supplier-specific. This method can also be applied to address the obsolescence likelihoods of supplier-specific part obsolescence events. Censored PDF and CDF distributions for procurement life (LP) shown in Figure 4.8.(B) can be generated from raw supplier-specific data (data for ON Semiconductor is shown in Figure 4.8.(A) using MLE as described in Section 4.1. 0 2 4 6 8 10 12 14 1994 1996 1998 2000 2002 2004 Introduction Date (D I) Pr o cu re m en t L ife (L P ) I n Y ea rs 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 Procurement Life (L P ) In Years Pr o ba bi lit y CDF PDF A BPr o cu re m en t L ife (L P ) I n Y ea rs Pr o ba bi lit y Figure 4.8 ? Supplier-specific procurement life data for linear regulators (ON Semiconductor): (A) raw obsolescence data from SiliconExpert; (B) censored PDF and CDF of obsolescence risk likelihood over time. 82 Note, the Weibull distribution, like most parametric fits, evolves over time as more data is accumulated. The method in described in Section 4.1 generates censored Weibull distributions to account for the fact that the data is right-censored, i.e., the dataset used in this study contains introduction dates for all parts, 347 of which have obsolescence dates and 509 of which were not obsolete as of 2008. The supplier- specific dataset for linear regulators from ON Semiconductor consists of 39 obsolete parts and 34 non-obsolete parts as of 2008. The censored CDF of LP (Figure 4.8.(B)) can be interpreted as the probability (likelihood) that a part will be obsolete Lp number of years after it is introduced. The supplier-specific CDFs will be used in Chapter 5 to estimate effective CDFs for second sourcing strategies. Similarly, the PDF of LP is the probability (likelihood) that a part will become obsolete during specific intervals of time after it is introduced. PDFs are used in Section 5.1, (5.1) to quantify obsolescence risk annually. Let ( )piF , be the supplier-specific CDF value in year i for supplier p. Then, the effective probability of obsolescence or CDF of a sourcing strategy, s where the part can be procured from SUPsN sources during year i can be calculated as shown in (4.8). ( ) ( )? = = SUP sN p SUP s piFNiF 1 ,, (4.8) Chapter 5 applies the CDF distributions of single sourcing and second sourcing combinations to assess and compare the obsolescence risk of various sourcing strategies. 83 4.3 Summary and discussion In this chapter, a methodology has been presented for constructing distributions that can be used to forecast the procurement lifetime, and thereby the obsolescence date, of technologies based on data mining the historical record. Unlike previous methods for forecasting DMSMS type obsolescence, this method is applicable to technologies that have no clear evolutionary parametric driver. Results from the methodology applied to several different electronic part types and sourcing strategies have been included. Long-term forecasting techniques generally involve methods of trend extrapolation. Although, trending the worst case procurement lives should be done using just the uncensored data (only the obsolete parts), trends in the mean procurement life must be done using the censored data set (both obsolete and non- obsolete parts) from Figure 4.7 corresponding to (4.6). It has been suggested that the ?age? of electronic parts is not necessarily a factor in determining what goes obsolete (Carbone 2003). The age of a part can be interpreted two ways; either it represents how long ago the part was introduced (DA - DI) where DA is the analysis date (DA - DI is referred to as ?design life? in Gravier and Swartz 2009), or how long the part was procurable for (LP). The results in this chapter suggest that age is a factor in predicting the obsolescence of the part for parts that do not have strong evolutionarily parametric drivers. Gravier and Swartz (2009) also conclude that age is correlated to obsolescence by showing that the probability of no suppliers varies with design life. However, Gravier and Swartz (2009) do not 84 distinguish between part types (except for military and non-military parts) or parts with or without strong evolutionary parametric drivers. For the procurement lifetime forecasting algorithms developed using the methodology suggested in this chapter to be useful, one must assume that past trends are a valid predictor of the future. In some cases, particular technologies or parts may be displaced by some unforeseen new disruptive technology, thus accelerating the obsolescence of the existing parts faster than what the historical record would forecast. Alternatively, new applications may appear that extend or create demand for specific technologies or parts also causing a change in the historical obsolescence patterns for the parts. Application of the proposed method depends on having access to sufficient historical data to support a statistical analysis; this is especially true when one wishes to refine the forecasts (to particular vendors or particular part attributes). The obsolescence date of a part or technology from the original manufacturer may or may not be a critical date in the management of a product or system depending on how the part or technology is used. Original manufacturer obsolescence dates when combined with the forecasted future need for the part and the available inventory of the part determine whether the obsolescence of the part is a problem or not, or when the obsolescence of the part will become a problem. For example, minimum buy sizes for many inexpensive electronic parts (e.g., resistors and capacitors) may far exceed the number of parts needed to manufacture and support a low-volume product, so the obsolescence of the inexpensive part may be a non-issue because the available supply of parts will never be exhausted. For a high- 85 volume product, the quantity of parts needed may quickly exceed what can be supplied by the existing inventory of parts and aftermarket suppliers, so forecasting the original manufacturers? obsolescence date is critical in order to enable strategic management of the product. 86 Chapter 5: Long-term sourcing risk model (DMSMS obsolescence) This chapter addresses DMSMS (Diminishing Manufacturing Sources and Materials Shortages) type obsolescence, which is defined as the loss of the ability to procure a technology or part from its original manufacturer (Sandborn 2008a). Forecasting when technologies and specific parts will become unavailable (non- procurable) is a key enabler for pro-active DMSMS management and strategic life cycle planning for long field life systems. However, knowing when a disruption will occur is only part of the problem. The impact or consequence of a disruption is often related to the timing of the event and must be considered in the assessment of sourcing strategies. Section 5.1 describes the method used to assess the risk that a sourcing strategy is exposed to. The example case study presented in this chapter utilizes the part TCO simulator to determine the consequence of an obsolescence event as part TCO (per part site). The part TCO simulator has been discussed in detail in Chapter 3. The obsolescence likelihood and consequence are then combined to quantify risk as an ?annual expected TCO per part site,? which is suitable for comparing various sourcing strategies over the part?s life cycle (period of time that the part is used within an organization). Section 5.2 utilizes effective CDF and PDF distributions to assess the tradeoffs between single and second sourcing strategies in terms of obsolescence risk. 87 5.1 Part sourcing risk The OEM?s total cost of ownership of introducing and supporting a group of suppliers, for parts in long life cycle products, can be combined with the estimated likelihood of disruption to quantify the risk of a part sourcing strategy as a function of time. Let ( )DsCTCO , be the total cost of ownership (TCO) when sourcing strategy s is selected and subject to a disruption date of D. Chapter 3 discusses the modeling approach for TCO with respect to the part sourcing strategy used. Let )(dFs be the CDF during year d of the part?s lifecycle with 00 =)(Fs . Chapter 4 discussed the method for estimating the CDF with respect to the sourcing strategy and combination of suppliers/sources. D is treated as discrete, )1()(}{ ??== dFdFdDP , and )(1}{ jFjDP ?=> . Note that D could be greater than j, in which case there is no disruption. In this case, the costs do not depend upon how much D exceeds j. Thus, we calculate the cost for 1D j= + to cover the case of no disruption. Then, ( )[ ]DsCE TCO , is the obsolescence risk as the expected TCO for sourcing strategy s after j years. ( )[ ] ( ) ( ) ( )( ) ( ) ( )( )? = ?++??= j d TCOTCOTCO jFjsCdFdFdsCDsCE 1 11,1,, Let CPPS be the part TCO per part site as calculated in (3.2) where VOLiN is the number of parts used by production/assembly activities in year i. Then the expected TCO per part site for sourcing strategy s after j years, ( )[ ]DsCE PPS , , is calculated as follows, 88 ( ) ( ) ( )( ) ( ) ( )( )? = ?++??= j d PPSPPS jFjsCdFdFdsCC 1 exp 11,1, ( )[ ] ? = = j i VOL i TCO N DsCE C 1 exp , (5.1) 5.1.1 Linear regulator case study The examples in this section apply the methodology to quantify obsolescence risk to study the sourcing of linear regulators. The case study focuses on three specific linear regulator manufacturers: Analog Devices, ON Semiconductor, and Texas Instruments (TI). For the example case in this section, the part TCO simulation model was populated with data (shown in Figure 5.1) from Ericsson AB for a generic linear regulator. The study quantifies the risk of single sourcing (from each supplier) and second sourcing (3 combinations of 2 suppliers) as well as compares the tradeoffs between each strategy. Using (5.1), the expected TCO per part site can be calculated. Part-specific inputs, non-part-specific inputs, and the characteristic part usage for the part within the OEM are shown in Figure 5.1 and are used in all the sourcing cases that follow. The example cases assume that when obsolescence occurs, the OEM performs a lifetime buy of the future projected demand plus a 10% buffer quantity. The lifetime buy is procured at the current price based on inflation and incurs inventory costs annually for the quantity kept in storage at the beginning of each year. The examples also assume that parts from all suppliers are introduced at year 0 and that parts must be supported until year 20 (j = 20 years). 89 Single Sourcing Example The right-censored PDF and CDF of single sourced linear regulators from the three suppliers are shown in Figure 5.2. The Weibull parameters for the three suppliers and their corresponding log-likelihood values are shown in Table 5.1. The expected part TCO per part site, (Cexp) is plotted over time (independent variable, d varied from 1 to j) in Figure 5.3 and 5.4 for price independent and price dependent cases respectively. 22 1 111 2 3 2 55 5 5 5 5 4 3 3 1 10 100 1000 10000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Year T o ta l a n n u a l p a rt sit e u sa ge (P ro du ct io n ) Number of products that the part is designed into T o ta l a n n u a l p a rt sit e u sa ge (P ro du ct io n ) Figure 5.1 ? Part TCO model inputs used in the example linear regulator case study (total production volume = 10,500 part sites). 90 Table 5.1. Supplier-specific censored Weibull distribution parameters, ? and ?. LKV is the negative log-likelihood function (larger negative values indicate a better fit). Weibull Parameters Texas Instruments ON Semiconductor Analog Devices ? (shape) 3.3299 3.9668 2.1858 ? (scale) 12.5831 11.0008 14.2503 LKV -69.917 -113.246 -39.424 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 Procurement Life (L P) In Years C D F TI (A) ON Semiconductor (B) Analog Devices (C) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 5 10 15 20 Procurement Life (L P ) In Years PD F C D F PD F Figure 5.2 ? Supplier-specific obsolescence likelihoods for linear regulators as (top) PDF and (bottom) CDF determined from historical data provided by SiliconExpert. The resulting Weibull fits are given in Table 5.1. 91 15 20 25 30 35 40 45 50 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Year Ex pe ct ed TC O pe r pa rt sit e (C ex p) TI On Semiconductor Analog Devices LTB for all parts at year 0 Part never goes obsolete Suppliers Part Number Price (per part) Cexp (at j = 20 years) Texas Instruments TPS720105DRVR $0.702 $17.19 ON Semiconductor NCP699SN30T1G $0.620 $17.11 Analog Devices ADP130AUJZ-0.8-R7 $0.990 $17.75 Figure 5.4 ? Cexp over time for single sourcing (price differences included for linear regulator example). 15 20 25 30 35 40 45 50 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Year Ex pe ct ed TC O pe r pa rt sit e (C ex p) TI ON Semiconductor Analog Devices LTB for all parts at year 0 Part never goes obsolete Suppliers Cexp (at j = 20 years) Texas Instruments $16.99 ON Semiconductor $16.99 Analog Devices $17.20 LTB for all parts at year 0 $20.05 Part never goes obsolete $16.52 Figure 5.3 ? Cexp over time for single sourcing (price-independent case for linear regulator example). 92 Figure 5.3 and 5.4 each show Cexp plotted over time for two special cases: 1) lifetime buy (LTB) for all parts at year 0 ? all the parts necessary to support all production forever are procured once at the beginning of the part?s life cycle as a lifetime buy for all future production demand, and 2) the part never goes obsolete ? the part never requires a lifetime buy and can be procured annually for the entire product life cycle. These two special cases describe bounding scenarios where life cycle cost is at extremes. When a lifetime buy is made at year 0, the total future production volume is stored in inventory from which parts for each year are drawn annually. Alternatively, when the part never goes obsolete, inventory cost is incurred only for the annual production quantity (assuming one purchase order is made every year for that year?s production volume). Additional parts may be purchased to replace failed parts or defective parts that have been diagnosed during assembly. The difference in Cexp between these two bounding cases is $3.53/part site after 20 years. Figure 5.3 shows Cexp plotted over time for a price-independent single sourcing case where parts are procured at $0.50/part from all suppliers in year 0 (includes deflation in part price of 2% annually). In this case, TI offers the lowest value of Cexp based on the right-censored CDF of obsolescence risk as expressed in Figure 5. The maximum difference in Cexp between these suppliers is $0.21/part site in 2010 dollars or 1.2% of Cexp of ON Semiconductor after 20 years. Figure 5.4 shows a price-dependent single sourcing case for specific linear regulator parts from each supplier. It is the same as Figure 5.3 except actual part prices are included. The maximum cost difference is $0.64/part site in 2010 dollars or 3.7% of Cexp of ON Semiconductor after 20 years. TI?s part, being a more expensive 93 part than ON Semiconductor?s by $0.082/part, exceeds ON Semiconductor in Cexp by $0.080/part site. The CDF value of ON Semiconductor?s part is the smallest of the three suppliers until year 6; as a result, the benefit to the overall TCO, for a slightly lower CDF early in the part?s life cycle, is almost equal to the cost of having a much higher CDF late in the part?s life cycle (year 8 to year 20). Statistically, this indicates that procuring parts from ON Semiconductor offers life cycle cost benefits over the other suppliers as a result of the part site usage and its effect on lifetime buy inventory cost. The part site usage shown in Figure 5.1 assumes an increase in part sites until year 6, a plateau between year 6 and 8, and a decline that follows thereafter. ON Semiconductor?s parts are least likely to go obsolete during periods of high part usage thereby reducing lifetime buy inventory cost. The single sourcing examples (Figures 5.3 and 5.4) show that, if you are going to single source linear regulators, there is no significant difference even with relatively large procurement cost differences. When parts are consumed in low volumes, procurement and assembly costs play a small part in the overall part TCO which are dominated by support costs instead. These examples show that low volume cases are insensitive to procurement price changes. However, for high volume part usage, price differences have a greater impact. An additional effect of high volume part usage is that large lifetime buys also lead to higher inventory cost, which enhances the benefit of selecting parts with longer procurement life. Therefore, for higher part production volumes, the procurement price of a part is expected to have an increasing role in sourcing tradeoffs. 94 Second Sourcing Example The potential advantage of second sourcing is that the parts can be purchased from two suppliers interchangeably. However, when second sourcing is used, both suppliers (and the parts they supply) are subject to approval and qualification processes within the OEM. The purpose of second sourcing is to ensure a continuous 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 5 10 15 20 Procurement Life (L P ) In Years CD F 10 100 1000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Year Ex pe ct ed TC O pe r pa rt sit e (C ex p) Second Source (A + C) Second Source (A + B) Second Source (B + C) TI (A) ON Semiconductor (B) Analog Devices (C) Second Sourcing (A + D) Annual expected cumulative TCO (Cexp) after 20 years @ $0.5/part: TI + ON Semiconductor = 33.01 per part site TI + Analog Devices = 32.92 per part site ON Semiconductor + Analog Devices = 32.98 per part site Figure 5.5 ? (left) CDF of obsolescence likelihood by sourcing strategy and (right) annual expected cumulative TCO per part site over time by sourcing strategy (price independent case for linear regulator example). 95 flow of parts and avoid ?down-time? (and related penalties) in the event of supply chain disruptions by offering a redundancy in the supply of parts. Essentially, the effective procurement life of a part that is purchased from more than one qualified supplier is the longest procurement life of all the suppliers used. Consider the following low-volume linear regulator case (shown in Figure 5.5) to demonstrate the tradeoff between single and second sourcing, as well as possible benefits in supplier selection based on obsolescence likelihood. The second sourcing example in Figure 5.5 assumes the following: 1) both suppliers are capable of supplying the total annual demand if necessary, 2) no competitive pricing or ?split- award? auctions are conducted (procurement price = $0.50/part), 3) no cost to switch between suppliers (once they are qualified), 4) every supplier must be qualified before being used (qualification cost = $100,000/supplier), 5) parts from both suppliers have the same introduction date (DI), and 6) learning indices, Bx, for support activities x, are assumed to be 0 (no learning from supplier-to-supplier, i.e., worst case). Figure 5.5 shows the calculated CDF distributions (left) and the corresponding obsolescence risk (right) over time to compare results between single sourcing (from Section 3.1) and their second sourcing combinations. Cexp after 20 years, for the second sourcing combination of TI and Analog Devices, is $32.92/part site. This combination is marginally lower than the combination of ON Semiconductor and Analog Devices, which yields a Cexp of $32.98/part site, due to the similarities between their second sourcing CDFs. However, the margin between Cexp is larger when second sourcing TI and ON Semiconductor due to consistently higher CDF 96 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 5 10 15 20 Procurement Life (L P ) In Years C D F Second Source (A + B) Second Source (B + C) Second Source (A + C) TI (A ) ON Semico nductor (B ) Analog Devices (C) Maxim Int egrated P roduct s (D) Second Source (A + D) Figure 5.6 ? CDF of obsolescence likelihood by sourcing strategy (linear regulators). values. In this case study, the savings (over single sourcing) associated with extending the effective procurement life of the part through second sourcing is negated by the high qualification and support cost related with utilizing a second supplier. The three suppliers, TI, ON Semiconductor, and Analog Devices, were selected to be used in the example case studies based on the completeness of the data set. Key factors in the selection of suppliers were the number of non-obsolete parts and the fraction of non-obsolete parts among the total number of supplier-specific data points. The outliers that exist within the linear regulator data set for which supplier-specific CDFs may be significantly different are a result of a high fraction of non-obsolete parts or a small number of valid data points within the supplier-specific data set (e.g., the CDF for Maxim Integrated Products is shown in Figure 5.6 is generated from a data set with 5 obsolete parts and 20 non-obsolete parts i.e., 80% 97 non-obsolete parts). I have included the Maxim supplier in the analysis that follows for demonstration purposes because it is significantly different than the other suppliers, however, the Maxim dataset has significantly fewer obsolescence events upon which to base a predictive forecast than the other suppliers. 5.3 Summary and discussions This section presents a method to quantify obsolescence risk in order to compare sourcing strategies of electronic parts used in long life cycle products and systems. Existing methods used to address sourcing for high volume, short field life products are procurement-centric focusing on procurement pricing, negotiation practices and purchase volumes. The method described in this chapter adopts a life cycle approach utilizing a part total cost of ownership model and historic obsolescence data to quantify obsolescence risk, which is suitable for comparing sourcing strategies over long life cycles. This chapter presents a calculation for ?expected part TCO (per part site),? which can be used as a metric to assess part risk. The methodology is applied in a comparison of single and second sourcing linear regulators from three suppliers: Texas Instruments, ON Semiconductor, and Analog Devices. The single sourcing cases for linear regulators show that the particular supplier parts are procured from (if the only difference is procurement life and procurement cost) does not make a significant difference even for relatively large procurement cost differences. It was also found to be difficult to make a business case for second sourcing linear regulators based only on maximizing procurement life (if the second source requires qualification). However, the method can be implemented 98 to identify the ideal combination of suppliers, from a life cycle perspective, if second sourcing is predetermined. 99 Chapter 6: Analytical part TCO model This chapter presents an analytical part TCO model based on simplifying assumptions that are valid for long-term sourcing of electronic parts used in long life cycle products. The analytical part TCO model estimates the part TCO subject to known supply chain disruption events. Section 6.2 discusses the implementation of the analytical part TCO model to assess cost tradeoffs between two sourcing strategies19 subject to part obsolescence (when the effective procurement lives are known). The method of comparing two sourcing strategies utilizes part TCO as a means to identify a ?break-even? learning index, B, necessary to make a particular multi-sourcing strategy (with Nsup available suppliers) viable. 6.1 Problem statement The part total cost of ownership (TCO) is the total cost spent at various stages of the part?s life cycle: procurement (CPROC), inventory (CINV), support (CSUP), assembly (CASY), and field failure repairs (CFF). Let TCOC be the part TCO calculated as shown in (3.1). This general form is the basis for the simulation part TCO model. FFASYSUPINVPROCTCO CCCCCC ++++= (6.1) Section 6.1 presents assumptions and the formulation of an analytical part TCO model applicable to sourcing parts for long life cycle product applications. The part TCO can be represented as ( )SUPsssTCO NBDC ,, . Let Ds be the effective disruption 19 This chapter considers only supply chain disruptions associated with the obsolescence of COTS parts. The formulation of a sourcing strategy refers to the selection and qualification of a finite number of suppliers from which the COTS parts may be procured. The word ?sources? refers to the part?s ?suppliers?. 100 date and let Bs be the learning index of all support activities when sourcing strategy s is adopted. The sourcing strategy s is defined by the number of suppliers/sources used, SUPsN . The difference in CTCO between different solutions that use different sourcing strategies (strategies a and b) is given by, [ ] ( )[ ] ( )[ ]bSUPbbbTCOaSUPaaaTCObaTCO NBDCNBDCC ,,,,, ?=? Let aD and bD be the part obsolescence dates (estimated from effective procurement lives) associated with the two sourcing strategies, a and b, being considered. The uncertainty associated with the effective disruption dates are addressed in Chapter 4 through the forecasting of procurement life distributions. The objective of this solution is to identify the ?break-even? learning index between two potential part sourcing strategies. From the context of this dissertation, learning indices for multi-sourcing support cost, B, are said to be at ?break-even? when the resulting TCO of the two sourcing strategies being compared, strategy a and strategy b, (subject to independent disruption dates) is equal; i.e., [ ] baTCOC ,? becomes zero. Determining a break-even learning index creates a target (for reducing qualification and support activities); a part management organization capable of achieving a learning index below the break-even learning index can be expected to benefit from the alternative multi-sourcing strategy. 101 6.2 Model assumptions and formulation In order to evaluate the analytical CTCO, several simplifying assumptions are made: 1. The cumulative part assembly cost, CASY is constant for a given part usage profile and is not affected by the sourcing strategy used. The total assembly cost, CASY, has been defined as being dependent on the part usage profile and the characteristics of the assembly process (yield as a result of defect testing, diagnosis, and rework). However, it is assumed that supplier-specific part quality (defect rates) are the same for all suppliers, therefore there is no change in the effective yield across the entire population of parts (i.e., INNININ SUPsYYY === ...21 ). The assembly cost is then independent of the number and selection of suppliers from which the part is procured. Subsequent equations include assembly cost in order to maintain proportionality in part TCO and can be simply calculated as described in (6.2) as a function of annual part usage, VOLiN . Note: part procurement price will be considered independent of the assembly cost henceforth. 2. The product warranty period is shorter than the part?s earliest possible wear-out failure under the expected operating conditions (most electronic parts, even in long field life applications, rarely reach wear-out). Failures due to infant mortality and random failures during the useful life are assumed to be negligible. Therefore, CFF = 0. Note, based on this assumption, the number of parts (procured) and number of part sites are equal (i.e., no replacement parts are needed). 102 3. Non-recurring support activities (such as qualification and validation) are all performed in year 1. 4. Learning indices, xiB are assumed to be constant for all organization-specific support activities, x, and do not change over time. For example, BBBB ni ap i as i ==== ... and BBBB x j xx ==== ...21 5. TCO over the product usage life cycle of the part is an accumulation of spending up to year j; cost saved or recovered (e.g., part salvaging) is not considered in the TCO model, i.e., CPROC ? 0, CINV ? 0, CSUP ? 0, CASY ? 0, CFF ? 0. 6. The number of suppliers, SUPsxiN , for a sourcing strategy s in year i does not change throughout the part?s procurement life cycle unless the part is no longer procurable from a particular supplier involved in the sourcing strategy (i.e., supplier-specific part obsolescence). For example, SUP sx SUP sxj SUP sx SUP sx NNNN ==== ...21 . Also, for a sourcing strategy, s, all suppliers require the same set of support activities x. Let the size of vector x (consisting of support activities) be n. Therefore, SUPsSUPsnSUPapsSUPass NNNN ==== ...,, . 7. The part price, SUPpiP is the same for all suppliers that parts are procured from (where supplier index, p goes from 1 to SUPsN ) and all the parts are subject to the same annual price change, i.e., SUPi SUP iN SUP i SUP i PPPP SUP s ==== ...21 . The following presents the formulation of the analytical part TCO model based on the seven assumptions stated above. Based on assumption 7, the total part 103 procurement cost from (3.11) when multi-sourcing can be simplified to its single sourcing form in Section 3.1.3 which assumes indifferent part prices across suppliers. ? = + = j i i s PROC i SUP i sPROC r)( DNPDC 1 1 )()( (6.2) The total part quantity procured from all suppliers in year i is, PROCiN , which is a function of effective disruption date, sD when sourcing strategy s is adopted, and annual part usage volume, VOLiN given by, ( ) ??? ??? ? >? =? 1), (6.5) reduces to, ( ) ( ) ( )[ ] ( ) ( ) ( ) ??? ? ??? ? ++?++=? ? = SUP b b N p B bSUPbINVbPROCaSUPaINVaPROCTCO pDCDCDCDCDCDCC 1 ( ) ( )[ ] ( ) ( )[ ] ( ) ( )[ ] ( ) ( )? = ? ?+?+?=? SUP b b N p B bSUP bSUPaSUPbINVaINVbPROCaPROCTCO pDC DCDCDCDCDCDCC 2 To obtain the break-even learning index, the learning index for sourcing strategy b (Bb) must satisfy the following equation where ?CTCO for the two sourcing strategies is 0. ( ) ( ) 0 2 =??+?+? ? = SUP b b N p B bSUPSUPINVPROC pDCCCC Solving (6.8) for the unknown variable, BBE, we get, ( ) ( ) ( )SUPb SUP b BE ,N bSUP SUPINVPROC N p B K DC CCCp 1 2 = ?+?+? =? = (6.8) where, BBE is the break-even learning index for sourcing strategy b. Substituting ?CTCO into equation (6.8), we get, ( ) ( )?? ? ?? ? ? = bSUP TCO ,N DC CK SUP b1 Equation (6.8) can be solved graphically to find the value of B at ?break- even?, BBE corresponding to ratio21, K, as shown in Figure 6.1. 21 Subscripts of ratio, K, denote the number of sources being used by the two sourcing strategies being compared. 109 Therefore, the cost tradeoffs between two sourcing strategies (irrespective of the number of suppliers) can be represented by costs from equivalent single sourcing cases as functions of learning indices and obsolescence dates. When solving (6.8), the introduction of a logarithm function results in there being real and imaginary solutions for break-even learning index, BBE. For the relationship in (6.7) and (6.8) to provide a real solution, K must be greater than 0. This condition implies that ?CTCO must be greater than 0. The correlation between learning index, BBE and the bounding limits for support cost, Csup are shown below. Case 1: ( )bSUP DC ? 0+ ( )( ) ?= +? bSUPBEC DCB 0sup lim -5 -4 -3 -2 -1 0 1 2 3 0 2 4 6 8 10 Ratio, K Le ar n in g In de x, B B E 2 suppliers 3 suppliers 4 suppliers 5 suppliers Figure 6.1 ? Plot of break-even learning index, BBE, with respect to the ratio, K = ?CTCO/Csup, at break-even (where TCO of a sourcing strategy with SUPbN number of suppliers is equal to the TCO of single sourcing). 110 Case 2: ( )bSUP DC ? ? ( )( ) ??= ?? bSUPBEC DCB sup lim The method to calculate the break-even learning index developed in this section is implemented in examples presented in Section 6.4 6.4 Comparison of analytical and simulation part TCO models (part TCO) This section presents example cases that compare the analytical and simulation part TCO models. This section will also identify the conditions under which results from the models diverge. Figure 6.2 shows the error in estimating part Figure 6.2 ? Error between the simulation and analytical part TCO models as difference in TCO (as a fraction of average TCO determined from the simulation and analytical part TCO models), with respect to the average procurement and inventory cost (as fraction of average TCO) for a low volume case (49,752 parts) and a high volume case (49,753,000 parts). 111 TCO using the simulation and analytical part TCO models for electronic parts. The results in Figure 6.2 show the error as a ratio with respect to average part TCO. The cost difference between the simulation and analytical models is an effect of increasing influence from field failure and assembly cost when part volumes increase. The cost difference, ?CTCO also increases as the fraction of procurement and inventory cost increases (the independent variable on Figure 6.2) but is negated by the growing average TCO cost in the denominator. The overall model error is also an effect of the total support cost. Both analytical and simulation models estimate support cost in the same way (no difference in the support cost models). When support cost dominates (when procurement and inventory cost is low for example), the total cost error is lower but is amplified by the low average TCO (in the denominator). The maximum observed error is less than 0.23% of part TCO. 112 Figure 6.3 ? Cost difference (per part site) between part TCO, CTCO and procurement/inventory cost, Cproc/inv with respect to total part usage volume after 20 years. Using the analytical part TCO model, Figure 6.3 shows the difference between part TCO, CTCO and procurement and inventory cost, Cproc/inv as a fraction of part TCO with respect to part usage volume. The difference is the error between modeling pure procurement cost and modeling part TCO. Figure 6.3 shows that larger error is observed at lower part usage volumes. The error is attributed to significant cost contributions from support, field failure, inventory, and assembly costs combined. The error diminishes as part volume increases. Figure 6.3 confirms that higher part usage volumes and/or higher part prices increase the relative cost from procurement (fraction of part TCO) thereby, reducing the error between part TCO and procurement cost models. In other words, pure procurement cost models lose accuracy at low part usage volumes justifying the need for part TCO models on which to base part management decisions. This section demonstrates the scale of the error 113 observed between the simulation and analytical part TCO models. Figure 6.2 show application-specific results where error at low volume part usage case is an order of magnitude lower than the error at the high part usage volume case. The level of error is dependent on the cost of procurement relative to the part TCO. Conversely, the level of error can be estimated as the combined cost from support, field failure, and assembly costs. Section 6.3 presents example cases using the analytical part TCO model to estimate the break-even learning index comparing single sourcing and second sourcing strategies. 6.5 Implementation of analytical part TCO model (break-even learning index) The analysis to compare sourcing strategies in Section 6.4 is useful when the parts management organizations are aware of the limitations in their capabilities and their ability to streamline support activities. For example, the analysis provides the organization a means to identify a viable multi-sourcing strategy that requires support cost learning indices, Bx, that are within achievable limits. This section discusses the comparison of two sourcing strategies in terms of TCO and disruption risk. The example cases will also estimate a break-even learning index subject to a learning index threshold, BTH imposed by the capabilities of the part management organization. The example problem addressed in this section can be stated as follows: 114 Figure 6.4 ? Inputs for the example case discussing the method in Section 6.3 (Lp is the part?s effective procurement life and DI is the part?s introduction date). ? Determine the break-even learning index, BBE for second sourcing linear regulators from two possible suppliers: A and B. The inputs for this example are shown in Figure 6.4. The part usage assumed for this case is shown in Figure 5.1. ? For a particular learning index, what is the maximum allowable inventory cost (per part) that makes a second sourcing strategy viable? ? Based on the uncertainty of disruption dates, determine the break-even learning index, BBE for second sourcing linear regulators from three possible suppliers: ON Semiconductor, Analog Devices, and TI. What is the probability that the required break-even learning index, BBE, will exceed a specified learning index threshold, BTH? The parameters for supplier-specific procurement life distributions (Weibull) are shown in Figure 5.1. 115 Figure 6.5 ? Part TCO (per part site) versus year of support for the example case where inventory cost is $0.1 per part. Figure 6.6 ? Part TCO (per part site) versus year of support for the example case where inventory cost is $10 per part. 116 Figure 6.7 ? Part TCO (per part site) versus year of support for the example case where learning index, B is 0 (maximum allowable inventory cost is $3.84 per part). Figure 6.5 and Figure 6.6 demonstrate the methodology to estimate the break- even learning index for second sourcing using the analytical part TCO model. The figures show the part TCO (per part site) with respect to the year of support (starting at 1). The example cases vary inventory cost for the part presented in Figure 6.4. For a predetermined inventory cost of $0.1 per part (per year), second sourcing is viable when learning index is B < -4.22. Similarly, when inventory cost is $10 per part (per year), the required learning index for second sourcing to be cost effective is B < 1.35. Consider a learning index threshold, BTH imposed on the part management organization22. The learning index threshold, BTH yields the ratio, KTH (derived from (6.8)) and vice versa, as shown below, 22 In order to minimize repeated support activities (reduce the ratio K and subsequently total support cost) in multi-sourcing strategies, the part management?s goal is to minimize learning index value (where -? < B < ?). The learning index may be determined by the level of qualification needed (either 117 ( )? = = SUP b TH N p B TH pK 2 where, ? 0, second sourcing is always a cost effective option. Figure 6.5 to Figure 6.7 show the second sourcing part TCO (per part site) when B = 0. For B = 0, the maximum allowable inventory cost is $3.84 per part (per year) for single sourcing and second sourcing strategies to ?break-even? as shown in Figure 6.7. based on product regulations or organizational policy) or practical capabilities (i.e., cost of resources used). 118 Figure 6.8 ? Break-even learning index, BBE versus inventory cost (per part per year) for the low volume example case discussed in Figure 6.4. If KTH = 1, then from (6.8) as applied to second sourcing, we get, ( ) 1? ?+?+? bSUP SUPINVPROC DC CCC ( ) ( ) ( )aSUPbSUPbSUPINVPROC DCDCDCCC +???+? ( )aSUPINVPROC DCCC ??+? (6.9) From (6.9), the key costs that drive the decision to single sourcing or second source the part under the ?worst-case? conditions discussed above are the difference in cumulative procurement cost (after j years), PROCC? , difference in cumulative inventory cost (after j years), INVC? , and the cumulative cost to support the part (after j years), SUPC subject to disruption date, aD . 119 Figure 6.10 ? Fraction of support cost repeated for second supplier (with respect to single sourcing support cost) at break-even, KBE vs. inventory cost (per part per year) with contour lines of varying procurement price for the low volume example case discussed in Figure 6.4. Figure 6.9 ? Break-even learning index, BBE versus inventory cost (per part per year) with contour lines of varying procurement price for the low volume example case discussed in Figure 6.4. 120 Results from Figure 6.8 to Figure 6.10 show the relationships between break- even learning index and price, inventory, and support costs. Figure 6.8 shows a plot of break-even learning index, BBE vs. inventory cost for a linear regulator part with a procurement price of $1. As inventory cost increases, the decrease in TCO is larger due to extending the effective procurement life from 5 years (single sourcing strategy a) to 10 years (second sourcing strategy b) thereby increasing the break-even learning index, BBE. For the example case, BBE > 0 when inventory cost exceeds $3.83 (per part per year) where second sourcing is the preferred sourcing strategy. Figure 6.9 shows a plot of break-even learning index, BBE versus inventory cost with contours for part price at varying orders of magnitude. Figure 6.9 shows that, when part price is high, cost of money increases the benefit of extending the part?s procurement life. When part price is approximately $100 (per part), second sourcing is preferred under all conditions of inventory cost. Similarly, Figure 6.10 shows the relationship between KBE (fraction of support cost repeated for the second supplier with respect to single sourcing support cost at break-even) vs. inventory cost. The given information allows the calculation of an exact break-even learning index that determines the feasibility of a multi-sourcing strategy. The following are Monte Carlo analyses for uncertain procurement lives in the second sourcing of linear regulators. These case studies deal with break-even learning index from the perspective of uncertain part procurement lives based on discussions from Chapter 4. Figure 6.11 to Figure 6.14 show results for the Monte Carlo analysis for varying inventory costs (linear regulator example case described in Figure 6.4). The results in Figure 6.11 show ratio, KBE comparing single sourcing and second 121 Figure 6.11 ? Monte Carlo results for inventory cost of $1 (per part per year) - probability of occurrence of KBE (CDF). sourcing strategies obtained using the method described in Section 6.3 for sampled procurement lives of three linear regulator vendors (TI (A), ON Semiconductor (B), and Analog Devices (C)) as discussed in Section 4.2. For each instance of the Monte Carlo sampling, the ratio KBE (and the corresponding break-even learning index, BBE) are calculated between the earliest and the latest disruption dates (i.e., this approach assumes that second sourcing is unbiased towards a particular). The distribution seen in Figure 6.11 is the probability (CDF) of occurrence of KBE between values of 0 and 1. 122 Figure 6.12 ? 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