ABSTRACT 
 
 
Title of Thesis: UTILIZATION OF DATA AND MODELS 
FOR COMMERCIAL OFF THE SHELF 
(COTS) ELECTRONIC COMPONENT 
SELECTION AND RELIABILITY 
ASSESSMENT 
  
 Edmond Elburn, Master of Science, 2018 
  
Thesis Directed By: Professor Michael G. Pecht & Dr. Diganta Das, 
Department of Mechanical Engineering 
The continued growth of commercial off-the-shelf (COTS) parts in electronic systems 
and hesitance of use in some applications necessitates the development of methods to 
evaluate part reliability. An information-based reliability evaluation method has been 
developed based on failure mechanism models incorporating application conditions 
and part parameters. The sources of the information necessary for COTS parts were 
identified along with the information these sources provide. The sources were 
contrasted with the information required for military, space, or automotive grade parts. 
Multiple methods of approximating the application conditions and part parameters 
were developed and incorporated into the reliability methodology along with the 
impacts of uncertainty levels on the reliability prediction. An evaluation of information 
availability was completed, and metrics were developed to quantify the thermal and 
material information provided for parts. An analysis of 22 COTS parts evaluated the 
metrics’ effectiveness, and reliability estimations compared the changes in part 
parameters and conditions. 
 
 
 
UTILIZATION OF DATA AND MODELS FOR COMMERCIAL OFF THE 
SHELF (COTS) ELECTRONIC COMPONENT SELECTION AND 
RELIABILITY ASSESSMENT 
 
by 
 
 
Edmond Elburn 
 
 
 
 
Thesis 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 
Master of Science 
2018 
 
 
 
Advisory Committee: 
Professor Michael Pecht, Co-Chair 
Dr. Diganta Das, Co-Chair 
Professor Patrick McCluskey 
Professor Peter Sandborn 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Acknowledgements 
 I would like to thank my advisors Dr. Diganta Das and Prof. Michael Pecht for 
providing continued assistance, challenging projects that have expanded my 
engineering problem solving skills, and constant feedback. I would also like to thank 
all of my committee members for providing value feedback and assistance near the end 
of my time in graduate school. I would like to thank everyone that attended and 
provided feedback during the morning meetings which was invaluable for my defense. 
I would also like to thank the many companies and organizations that sponsored 
projects and provided unique ways to learn and solve problems. 
 I am extremely grateful for the work and assistance that the fellow graduate 
students, research faculty, and interns provided that helped me complete work towards 
my thesis. Dr. Utter, thank you for providing feedback throughout my entire time at the 
Center for Advanced Life Cycle Engineering, being a great friend, and sharing many 
stories that were always good for a laugh. To my friends, thank you for always 
providing a way for me to relax and escape the research grind. Thanks to the trivia team 
for a great time even if our final score was never the best. 
 To my parents, thank you for always helping me get to this point. I may have 
always wanted to be an engineer but without your continued support and help I would 
not be the person I am today. From helping me with 4th grade math homework to 
helping me select a college to listening to me talk about my research at our trips to The 
Cheesecake Factory, I am who I am because of you guys.  
ii 
 
 
 To Chance, thank you for being an amazing friend and loving girlfriend. Thank 
you for always listening to my research ramblings, providing feedback, keeping me 
focused, being understanding, and tolerating my love for the same few restaurants. 
Your support was invaluable to me. 
iii 
 
 
Table of Contents 
Acknowledgements ....................................................................................................... ii 
Table of Contents ......................................................................................................... iv 
List of Tables ................................................................................................................ v 
List of Figures .............................................................................................................. vi 
List of Abbreviations and Acronyms ......................................................................... viii 
Chapter 1: Introduction ................................................................................................. 1 
Chapter 2: Evaluating Reliability of Electronic Parts ................................................. 10 
Chapter 3: Information Requirements for Modeling .................................................. 18 
Application Conditions ........................................................................................... 18 
Sensor Collected Information ............................................................................. 19 
Derating Conditions Approximation Method ..................................................... 27 
Part Information Sources ........................................................................................ 29 
Commercial Sources ........................................................................................... 30 
Commercial Part Information Templates............................................................ 36 
Node Size Approximation Method ..................................................................... 38 
Higher Grade Part Information ........................................................................... 40 
Modeling Constants ................................................................................................ 44 
Time Dependent Dielectric Breakdown Modeling Constant Analysis ................... 47 
Chapter 4: Information Availability Metrics .............................................................. 52 
Thermal Information Availability (TIA) ................................................................ 54 
Material Information Availability (MIA) ............................................................... 58 
Metrics Value Usage ............................................................................................... 61 
Reliability Estimation Incorporation................................................................... 61 
Comparison of Parts ............................................................................................ 63 
Generalization and Comparison of Manufacturers or Part Types ...................... 64 
Verifying and Adjusting Multiplier Level Values .................................................. 66 
Case Study Analysis ............................................................................................... 67 
Chapter 5: Software Implementation and Analysis .................................................... 79 
Single Part Reliability Estimation ........................................................................... 82 
Comparison of Failure Distribution with Different Part Parameter ........................ 85 
Comparison of Different Temperature Distribution Approximation Methods ....... 87 
Comparison of Temperature Information Availability Values on Failure 
Distributions ............................................................................................................ 90 
Evaluation of Different Sample Sizes ..................................................................... 91 
Chapter 6:  Contributions and Future Work ............................................................... 93 
Appendices .................................................................................................................. 95 
Appendix A: Time to Failure Distribution Python Code ........................................ 95 
Bibliography ............................................................................................................. 100 
 
iv 
 
 
List of Tables 
Table 1:Definitions of COTS collected from various sources ...................................... 2 
Table 2: New parts released by Texas Instruments (March – September 2018) [12]. .. 4 
Table 3: Comparison of different part type costs and availability ................................ 5 
Table 4: Sample semiconductor failure mechanisms and associated models ............. 17 
Table 5: Derating guidelines for transistors provided by NASA [42] ........................ 27 
Table 6: Comparison of application condition collection methods ............................ 29 
Table 7: Summary of information sources for COTS electronic parts ....................... 30 
Table 8: Most common terms and their frequency of occurrence in Vishay and ON 
Semi Technical Libraries ............................................................................................ 35 
Table 9: MIL-PRF-38535 QML Class and Descriptions ............................................ 43 
Table 10: Example standards for different military test qualifications ....................... 44 
Table 11: TDDB Time to failure data collected from research papers for TDDB (each 
region are results from a different part). ..................................................................... 45 
Table 12: Impact of Node Size on Electric Field Parameters [33] ............................. 47 
Table 13: Modeling Parameters for activation energy [38]. ....................................... 49 
Table 14: Usable temperature range and corresponding 𝛼 value for different energy 
levels [38].................................................................................................................... 50 
Table 15: Comparison of Information Provided for Vishay COTS Parts ................... 52 
Table 16: Information Availability for Parameters from Infineon MOSFETs Part 
Selection Table............................................................................................................ 53 
Table 17: Location multiplier levels ........................................................................... 55 
Table 18: Thermal resistance & power dissipation levels .......................................... 55 
Table 19: Temperature rating multiplier levels .......................................................... 55 
Table 20: Access multiplier levels .............................................................................. 60 
Table 21: Content multiplier levels............................................................................. 60 
Table 22: List of parts for case study analysis ............................................................ 67 
Table 23: Part numbers with associated categories .................................................... 68 
Table 24: Thermal information collected for parts ..................................................... 69 
Table 25: Statistical analysis of part category TIA and MIA values. Highlighted red 
and green values are lowest and highest mean values subsequently. ......................... 74 
Table 26: Statistical analysis of MIA and TIA values for different manufacturers .... 77 
Table 27: Sample Part Part Parameters and Model Constants .................................... 82 
Table 28: Time to X% Failure for Different Oxide Thickness (all other inputs held 
constant) ...................................................................................................................... 86 
Table 29: Comparison of Time to X% Failure for Different Temperature Distribution 
Approximation Methods ............................................................................................. 89 
Table 30:  TIA Comparison Percentage Failure Time to Failure Distribution ........... 91 
Table 31: Time to X% Failure for Different Output Sample Sizes ............................ 92 
 
v 
 
 
List of Figures 
Figure 1: Process flowchart for estimating COTS part reliability using information ... 8 
Figure 2: Bathtub curve for a part representing the hazard rate over time ................. 11 
Figure 3: Sample Texas Instrument Part Reliability Information ............................... 14 
Figure 4: Example constant failure rate information provided by part manufacturer (ON 
Semi) with listed assumptions on activation energy, confidence level, and application 
die junction temperature. ............................................................................................ 15 
Figure 5: Processor temperature measured during usage compared with datasheet 
maximum value. .......................................................................................................... 20 
Figure 6: Comparison of different bandwidth (h) values on a gaussian kernel density 
function generated from 2000 samples with mean of 5 and standard deviation of 1. 22 
Figure 7: Process for converting input samples to output samples through distribution 
approximation. a) provides (randomly generated) temperature samples, b) shows the 
kernel distribution estimation and corresponding bins, c) converts the distribution into 
a cumulative form and shows randomly generated points between [0,1] and the 
corresponding bins that they fall in, d) shows the final sampled values compared with 
the kernel distribution. ................................................................................................ 24 
Figure 8: Collected temperature sample readings from Intel I7-8550U processor. .... 25 
Figure 9: Comparison of different kernel bandwidths for approximating temperature 
distribution. Input samples histogram converted to a discrete probability distribution.
..................................................................................................................................... 26 
Figure 10: Comparison of different kernels for approximating a sample temperature 
distribution. ................................................................................................................. 27 
Figure 11: Information provided within the part number for an Intel processor [52]. 32 
Figure 12: Sample curve of the impact on turn on voltage with respect to temperature 
[43]. ............................................................................................................................. 33 
Figure 13: Part information required for failure mechanism template (TDDB) ......... 37 
Figure 14: Application condition information for failure mechanism template ......... 38 
Figure 15: Change in most currently developed node size in each year. .................... 39 
Figure 16: Change in oxide layer thickness in relation to node size. ......................... 40 
Figure 17: Availability of PPAP documentation for Diodes Inc. MOSFETs ............. 42 
Figure 18: Predicted vs actual time to failure using optimized model constant values.
..................................................................................................................................... 47 
Figure 19: Relation of activation energy and electric field over two different bond 
energy levels. .............................................................................................................. 49 
Figure 20: Relationship of activation energy and node size ....................................... 49 
Figure 21: Relation of gamma parameter and temperature over different electric fields 
and energy levels [38]. ................................................................................................ 50 
Figure 22: Relation of gamma parameter, temperature, and oxide layer thickness. ... 51 
Figure 23: Common temperature measurement locations in a part. ........................... 56 
Figure 24:Sample IPC 1752 document for MOSFET [70]. ........................................ 59 
vi 
 
 
Figure 25: Summary of comparison methods for generalizing metric values ............ 65 
Figure 26: Comparison of minimum and maximum operating temperature values for 
each part ...................................................................................................................... 70 
Figure 27: Part TIA rating value and TIA conversion value for the sample part list . 71 
Figure 28: Final TIA Value for different categories of parts ...................................... 72 
Figure 29: Comparison of MIA content and access multiplier values for each part .. 73 
Figure 30:  Comparison of MIA and TIA values for each part .................................. 75 
Figure 31: Euclidian distance similarity between parts based on TIA and MIA value 
(higher numbers are less similar) ................................................................................ 76 
Figure 32: Euclidian distance similarity between Texas Instruments parts (higher 
numbers are less similar) ............................................................................................ 78 
Figure 33: Software Implementation flowchart with information sources (blue circles) 
and hyper parameter (red text). ................................................................................... 79 
Figure 34: Sample time to failure distribution (simulated data) showing analysis of time 
to certain percentage of failures (red line) and the probability of failure for a certain 
length of time (orange dashed line). ........................................................................... 81 
Figure 35: Simulated application condition information for TDDB mechanism model 
parameters. .................................................................................................................. 83 
Figure 36: Comparison of input and output samples using kernel density distribution 
approximation method. The top plot shows the input samples and the kernel density 
that was approximated (black line). The bottom plot shows the final samples generated 
using the kernel density distribution. .......................................................................... 84 
Figure 37: Time to failure distribution for a single part generated from 5000 samples 
from application condition distributions. Dashed lines show the time at which 1%, 5%, 
and 50% of all samples will fail. ................................................................................. 85 
Figure 38: Projected TDDB time to failure for different oxide thicknesses (all other 
inputs remained constant). Gate voltage of 1.08 determined by using relationships 
between oxide thickness, node size, and gate voltage (see Chapter 3). ...................... 86 
Figure 39: Comparison of collected temperature information and processor maximum 
junction temperature. .................................................................................................. 87 
Figure 40: Comparison of measured values kernel approximation distribution, assumed 
normal distribution below the maximum junction temperature, and the maximum 
junction temperature. .................................................................................................. 88 
Figure 41: Comparison of TDDB time to failure distribution for different temperature 
distribution approximation methods. The Junction distribution was determined by 
using a constant value of 100 ℃ for all samples. ....................................................... 89 
Figure 42: TIA Comparison Failure Distributions...................................................... 90 
Figure 43:Comparison of different sample sizes on failure distribution .................... 92 
 
vii 
 
 
List of Abbreviations and Acronyms 
CAS Chemical Abstracts Service 
COTS Commercial off the Shelf 
FMMEA Failure Mode, Mechanism, and Effect Analysis 
IGBT Insulated Gage Bipolar Transistor 
MIA Material Information Availability 
MOSFET Metal Oxide Semiconductor Field Effect Transistor 
MSL Moisture Sensitivity Level 
PPAP Production Part Approval Process 
TIA Thermal Information Availability 
QML Qualified Manufacturer List 
QPL Qualified Products List 
 
viii 
 
 
Chapter 1: Introduction 
Almost every engineered system and piece of technology in the world today 
utilizes, is managed by, or is controlled using an electronic system. Each electronic 
system contains individual parts that have specific functionality. As electronic systems 
continue to grow and expand into new areas and aspects of life, ensuring proper 
performance and reliability continually becomes more important and crucial.  
Electronic parts and systems have been used for many years in commercial, 
industrial, military, medical, aerospace and many other applications. Each of these 
applications has specific requirements and factors that distinguish it from others such 
as environmental conditions, reliability requirements, and design time. Historically, 
different grades of parts have been developed and qualified by part manufacturers for 
specific application, such as space, automotive, or military grade parts. With the 
continued growth of commercial applications and reduction in availability of “higher” 
grade application parts, the use of commercial off the shelf (COTS) parts are a likely 
source going forward to fill the need for military, space, and other users. 
There is no single accepted definition for COTS devices. Each organization, 
manufacturer, or person has their own interpretation of the acronym that is different. 
Frequently, the differences are based off the intended application or use. Table 1 lists 
some different definitions provided for commercial off the shelf parts, systems, 
software, or designs.  
1 
 
 
Table 1:Definitions of COTS collected from various sources 
Organization / Person Definition 
“If you can buy it from a catalog without modification it is 
Fairchild Defense [1] 
COTS” 
Society of Automotive Engineers “An electronic component developed by a supplier for 
(SAE) / NASA Jet Propulsion Lab multiple customers, whose design and configuration are 
(JPL) [2] controlled by the supplier’s or an industry specification.” 
A commercial item sold in substantial quantities in the 
commercial marketplace; and offered to the government, 
Federal Acquisition Regulation 
under a contract or subcontract at any tier, without 
(FAR) [3] 
modification, in the same form in which it is sold in the 
commercial marketplace. 
“COTS is generally defined for technology, goods and 
services as: a) using commercial business practices and 
COTS Journal [4] specifications, b) not developed under government funding, 
c) offered for sale to the general market, d) still must meet 
the program ORD” 
Not subject to design or specification requirements that are 
IEEE Requirements for Replacement unique to nuclear power plants, used in applications other 
Parts for Class 1E Equipment in than nuclear power plants, and ordered from the 
Nuclear Power Generating Stations manufacturer/supplier on the basis of specifications set forth 
[5] in the manufacturer’s published product description (for 
example, a catalog). 
ISO/IEC/IEEE Systems and software 
“Product available for purchase and use without the need to 
engineering -- Content of life-cycle 
conduct development activities.” 
information products [6] 
“Software or hardware that is commercially made and 
UMD: Center for Public Policy and available for sale, lease, or license to the general public and 
Private Enterprise [7] that requires little or no unique government modifications to 
meet the needs of the procuring agency.” 
“Any grade [component] that is not space qualified and 
NASA [8] 
radiation hardened.” 
 
Based off the definitions from various sources, COTS devices are defined as 
parts developed for multiple customers where design and specifications (testing, 
ratings, documentation, process change policies) are established and controlled solely 
by the part manufacturer. The part manufacturer will select the part specifications 
2 
 
 
without specific input from an end user and the part is not qualified for a specific 
application.  
There are two major categories of parts that do not fall within the definition for 
COTS devices. Parts that have been qualified for military, space, or automotive 
standards specifically are not considered COTS parts. Additionally, “custom” parts that 
are specifically designed for a unique customer are also not COTS devices. There are 
unique situations that blur the lines between these like “enhanced” products provided 
by part manufacturers that are commercially available, designed for military or 
aerospace applications, but do not meet all of the qualification requirements of QML 
devices [9], [10].  
The motivation for using COTS devices in higher grade applications has been 
attributed to many factors [11]. The increased demand of commercial applications has 
resulted in COTS devices having the most advanced technologies and largest scale of 
production. Alongside the increase in commercial parts has been a decrease in military 
and space parts due to the small number of purchases and more demanding and 
complex design considerations. COTS parts are available for a lower cost than military 
or space grade parts on a per unit basis. COTS parts are provided through more 
distributors resulting in better availability and flexibility for users. COTS parts have 
better process control due to the higher production scale.  
The newest technological parts are primarily released COTS versions. For 
example, Texas Instruments released 151 COTS parts between March and September 
of 2018, compared with only one space or military qualified part during that same 
3 
 
 
period of time (see Table 2 for detailed overview) [12]. Texas Instruments is known as 
one of the largest semiconductor part manufacturers and has provided military and 
space qualified parts for over 60 years [13]. Analog devices, who also provide military 
and space qualified parts, has only released one new aerospace part design in the last 6 
months compared with 46 new COTS parts [14]. 
Table 2: New parts released by Texas Instruments (March – September 2018) [12]. 
Part Rating (By Texas Hi-Reliability Space / 
COTS Automotive 
Instruments) (COTS+) Military 
Amplifiers 22 7 0 0 
Audio 5 2 0 0 
Clock and Timing 3 0 0 0 
DLP Chipsets 0 1 0 0 
Data Converters 12 1 0 1 
Interface 29 1 0 0 
Isolation 1 0 0 0 
Logic 2 1 0 0 
Microcontrollers 9 0 0 0 
Motor Drivers 5 1 0 0 
Power Management 47 12 0 0 
Processors 2 0 0 0 
RF and Microwave 2 0 0 0 
Sensors 9 0 0 0 
Switches and Multiplexers 3 0 0 0 
Total 151 26 0 1 
 
Another assumption is that COTS parts are more readily available and at a lower 
cost than equivalent non-COTS parts. This was evaluated by comparing similar parts 
of different part types (COTS vs non-COTS) and evaluating the cost and availability. 
Three comparisons have been made based off parts with different ratings but the same 
functionality (summary of results in Table 3). The non-COTS parts are on average over 
5x more expensive than the equivalent COTS parts. Additionally, the COTS parts had 
4 
 
 
over 10x more availability from multiple distributors, whereas the non-COTS were 
only available from a single overstock distributor. 
Table 3: Comparison of different part type costs and availability 
Unit Cost / Total Min Order Authorized 
Part Category Part Rating 
100 Units Inventory Quantity Distributors 
Differential COTS $2.05 > 5,000 n/a 3 
Comparator Military $21.16 537 n/a 1 (Overstock) 
PWM COTS 32.16 1,000 – 5,000 1 3 
Controller Space 433.97 35 20 1 (Overstock) 
BJT COTS 4.31 > 40,000 5 4 
Transistor Space 15.15 0 100 1 
 
There had been an assumption that military or space grade parts (non-COTS) 
are reliable in demanding applications [15], but this does not exist for COTS parts. This 
assumed reliability comes from decades of use and standardized qualification and 
screening processes that are completed before and while the part is in use. Due to COTS 
devices not having the same standardized qualification process, there has been 
hesitation towards use. Thus, a s additional tests are completed by users to ensure that 
COTS can meet the needed reliability for space or military applications [16]. This 
reduces the cost benefit associated with using COTS part in military or space 
applications [17]. The additional evaluation period and testing has made it difficult to 
use COTS devices in higher grade applications and necessitates the development of 
new reliability estimation methods. Additionally, there is an assumption that the 
information provided by non-COTS parts is more detailed, of higher quality, and more 
readily available than for COTS parts.  
5 
 
 
Space applications have high reliability expectations due to long mission times 
and required functionality in a single instance. Additionally, the increased risk of 
radiation-based failure mechanisms means that the reliability evaluation of parts for 
space applications is completed rigorously and historically only space qualified parts 
have been used. COTS parts do not complete the additional qualification testing 
associated with radiation failure mechanisms. Various articles have evaluated the 
reliability of COTS parts in space applications by determining the susceptibility of 
COTS parts to radiation through physical and simulated testing [17]–[20].  
A subset of space programs and applications are non-safety critical such as 
CubeSat. These missions operate on lower budgets and can utilize the more advanced 
technology and lower cost benefits of COTS parts. Numerous project reports have been 
documented based on the process used to implement COTS parts into space 
applications and what challenged and observations were found [2], [11], [16], [21]–
[24]. NASA has used COTS parts in aerospace applications in specific instances. 
NASA balances the criticality and severity of the mission as well as the expected 
lifetime requirements when determining whether to use COTS parts or not. NASA 
traditionally completed an up-screening process when qualifying a COTS part for a 
specific space applications including satellite and rover systems [8]. Depending on the 
criticality of the mission and the environmental conditions the part will be used in, 
additional testing, fault tolerant designs, and / or radiation hardening may be required 
[8].  
6 
 
 
In addition to reliability concerns, less information is historically assumed to be 
available for COTS devices compared with aerospace and military grade devices [2]. 
Due to the standardized development process and long-term usage, military and space 
grade parts have historical usage data, lessons learned from previous part iterations, 
and have been evaluated for specific failure mechanisms like radiation impact that 
COTS devices have not been. This perceived lack of information has made it difficult 
for military and space customers to consider COTS devices without a detailed analysis 
to ensure proper performance. 
An information-based reliability assessment is utilized to evaluate the reliability 
of COTS devices in space or military applications and incorporates the information that 
can be found for the part. This will be completed using physics of failure-based models 
that are dependent on part specific attributes, application conditions, and modeling 
constants. The implementation is based on Monte-Carlo sampling, meaning that each 
information input is considered a distribution and thus the resultant time to failure is a 
distribution which can be analyzed. A summary of the process is provided in Figure 1. 
7 
 
 
 
Figure 1: Process flowchart for estimating COTS part reliability using information  
The outline of this thesis is as follows. First, the motivation for using reliability-
science methodology is discussed in Chapter 2 and used to determine the information 
that must be found to estimate reliability. This chapter also includes a discussion and 
critique of the constant failure rate reliability methodology that is still used in industry 
to this day. Chapter 3 discusses information collection methods for the inputs needed 
for using the physics of failure methods, including an analysis of the information that 
is available for COTS and non-COTS devices. Chapter 4 defines information 
availability metrics based on thermal and material documentation for COTS devices 
and how to implement them in the time to failure estimation method, including a case 
study analysis with 22 COTS parts that are to be used in an aerospace application. 
Chapter 5 presents the time to failure estimation method and results comparing 
8 
 
 
different information sources and values. Finally, contributions and recommendations 
for future work are provided in Chapter 6. 
  
9 
 
 
Chapter 2: Evaluating Reliability of Electronic Parts 
Reliability is the ability of a product to meet performance specifications without 
failure in for a certain length of time in specific application conditions [25]. The 
classical method of calculating reliability of a part or system assumes of a constant 
failure rate. The constant failure rate assumption implies that the rate of failures will 
not change over the part’s entire lifetime. This assumption is known to be false.  
The reliability of a part is determined based on many factors including the 
manufacturing quality, design, and application in which it is used. The life of a part is 
approximated using the bathtub curve (shown in Figure 2) which highlights three main 
regions based on the hazard rate: infant mortality, useful life, and wearout. The hazard 
rate is the probability of the first failure of a part. Infant mortality failures typically 
occur due to manufacturing defects. The useful life period is when the hazard rate is at 
its lowest and failures that occur during this period are typically random. The final stage 
is the wearout period. This region features an increasing failure rate over time as the 
device reaches the end of its designed life. The bathtub curve is an approximation and 
still does not account for all situations. For example, a part used in a high stress 
environment can lead to a wearout failure occurring early in the life.  
10 
 
 
 
Figure 2: Bathtub curve for a part representing the hazard rate over time 
The most common (constant) failure rate metric is the failures in time (FIT) 
rate. This value determines the number of parts that are expected to fail per billion 
hours of usage up to a certain confidence level. The method of determining the constant 
failure rate value is based on many assumptions that rarely hold and are not 
generalizable for different application conditions. Many manufacturers use JESD85 
[26], a standard for determining FIT rates (failures per billion hours) which uses the 
following process: 
1. Test parts in high stress environments that accelerate the rate of failures. The 
assumption is made that parts tested at high temperatures will still fail by the same 
method as if they were tested in a less stressful environment.  
2. Apply the Arrhenius equation to determine the acceleration factor (AF) between 
the high-stress levels and an assumed normal condition (an activation energy level 
must also be assumed in this step). The Arrhenius equation (with a temperature 
dependency relationship) is provided in equation 1.  
11 
 
 
𝐸𝑎 1 1
𝐴𝐹 = exp (− ( − ))  (1)  
𝑘 𝑇1 𝑇2
where 𝐴𝐹 is the acceleration factor, 𝐸𝑎 is an assumed activation energy (most 
commonly selected as 0.7 eV), 𝑘 is Boltzmann’s constant, and 𝑇1 / 𝑇2 are accelerated 
and selected normal usage conditions.  
3. Determine the equivalent device hours (EDH) by multiplying the acceleration 
factor by the total testing time in the accelerated state (𝑇𝑖𝑚𝑒𝑎𝑐𝑐𝑒𝑙). This formula is 
shown in equation (2). The assumption is also made that the total acceleration time 
is the sum of all individual part times that have been tested in the stressed state.  
𝐸𝐷𝐻 = (𝐴𝐹)(𝑇𝑖𝑚𝑒𝑎𝑐𝑐𝑒𝑙)  (2)  
4. Convert the number of failures with the chi-squared distribution using the number 
of samples and a selected confidence level (typically 60% or 90% for 
manufacturers). The assumption is made that failures occur immediately after 
testing is ended when using the chi-squared distribution.  
𝜒2(𝛼, 𝜈)
𝑀 =   (3)  
2
where 𝑀 is the projected number of failures following the chi-squared distribution with 
confidence level of 𝛼 and 𝜈 = 2 ∗ 𝐹𝑎𝑖𝑙𝑢𝑟𝑒𝑠 + 2. 
5. Determine the failure rate (𝜆) by dividing the chi-squared value (𝑀) by the 
equivalent part hours (and multiply by 109 if converting to FIT rate).  
12 
 
 
𝑀
𝜆 =   (4)  
𝐸𝐷𝐻
𝐹𝐼𝑇 = 𝜆 ∗ 109  (5)  
One key aspect to this process is the conversion from accelerated to normal 
conditions using the Arrhenius equation (and any assumed activation energy). The 
activation energy is process specific and cannot be generalized for entire families of 
parts. The activation energy for an electromigration related failure is not the same as 
the activation energy for a dielectric breakdown process and must be distinguished. The 
construction, design, material properties, manufacturing, and usage will all impact the 
mechanism of failure and change the activation energy. 
Another important aspect to determining the constant failure rate is the 
projected number of failures using the chi-squared distribution. This methodology is 
used because in many cases there are no failures observed during the testing. How can 
an accurate failure rate be determined if there are no or very few observed failures in 
the testing? For example, a Texas Instruments reliability information table is provided 
in Figure 3 and shows that there were 0 failed parts out of the 24,231 samples that were 
each tested for 1000 hours at 125 ℃. The  MTBF (mean time between failures) and 
FIT rate are provided for the part based on the assumptions within the chi-squared 
distribution, confidence level, and application temperature. 
13 
 
 
 
Figure 3: Sample Texas Instrument Part Reliability Information 
Because a constant failure rate (and thus exponential failure distribution) is 
assumed, manufacturers can test many parts and convert it into an estimation on the 
failure rate for a single part number. The assumption is completed with the equivalent 
part hours conversion (step 3). Part manufacturers also complete this process for entire 
families of parts, even if this assumes that every part will have the same activation 
energy level and failure rate, which is not true. For example, ON Semi publishes the 
failure rate data for each of their families of parts, even if individual parts have a 
different design [27]. They even assume the same activation energy for all the different 
families of parts. An example document provided by ON Semi is shown in Figure 4. 
Vishay also provides reliability reports and the same failure rate values for part groups 
such as all N-channel MOSFETs [28]. These broad assumptions ignore the differences 
in designs, materials, and even technology levels, which would result in differences in 
dominant failure mechanisms. Because of these assumptions and lack of accounting for 
application conditions, it is not recommended to use failure rate data for projecting 
reliability metrics and instead consider potential failure mechanisms and associated 
models.  
14 
 
 
 
Figure 4: Example constant failure rate information provided by part manufacturer 
(ON Semi) with listed assumptions on activation energy, confidence level, and 
application die junction temperature. 
Only through determining the failure mechanisms for the part based off the type 
of usage and application conditions can the reliability be estimated, and appropriate 
risk mitigation performed. A failure mechanism is the physical, chemical, electrical, or 
other process by which a part fails and is fundamentally related to physical 
characteristics of the part [25]. Using failure mechanisms allows for a better 
representation of how the part can fail and thus better modeling method. 
The reliability of a product is entirely dependent on the application and 
conditions in which the part is used. A COTS part that is reliable for a commercial 
application need not be considered reliable in a military or space application. To reduce 
15 
 
 
the need for qualification testing, an information-based reliability method is completed 
based on specific failure mechanisms associated with the part. 
A failure mechanism is the root cause behind why the part has failed and is 
fundamentally related to the physical properties of the device [25]. In this thesis, die-
level semiconductor failure mechanisms and associated failure models are considered 
[29]. A failure model is connected with each failure mechanism to predict a reliability 
metric (like time to failure) based on specific parameters. Each failure model requires 
information about the part and the application in which the part is used. To illustrate 
this point, an analysis of the information required for the time dependent dielectric 
breakdown (TDDB) failure mechanism is presented. 
TDDB is based on the thermal bond breakage at the Si - Si𝑂2 barrier due to the 
electric field that is generated in a transistor. Silicon – oxygen bonds are broken, 
leading to oxygen vacancy and generation of weak Si – Si bonds that weaken the oxide 
layer and result in eventual breakdown. This process is more prevalent with higher 
electric fields and higher temperatures which are the environmental stress factors. The 
form of the model and the explanation of the variables are provided in equation  6. 
𝐸𝑎𝑎
𝑇𝑇𝐹 = 𝐴0 exp(−𝛾𝐸𝑜𝑥) exp ( )  6  𝑘𝑇𝑗
where TTF is the time to failure of the device, 𝐴0 is an arbitrary scaling factor, 𝛾 is the 
electric field acceleration factor, 𝐸𝑜𝑥 is the externally applied electric field, 𝐸𝑎𝑎  is the 
apparent activation energy for specifically TDDB, 𝑘  is Boltzmann’s Constant, and 𝑇𝑗 
is the junction temperature in kelvin. 
16 
 
 
Equation 6 can be altered by modifying the electric field into the ratio of the 
operating voltage and the oxide layer thickness of the part. Using this conversion, the 
model is now dependent on the part parameters of oxide layer thickness and activation 
energy (for TDDB), application condition parameters of junction temperature and 
operating voltage, and model parameters 𝐴0 and 𝛾. 
The model constant values are part dependent and cannot be generalized. 
Extensive research has been completed on specific parts to determine model constants 
that accurately project the time to failure for TDDB [30]–[38]. Using this information, 
ranges on the modeling constants have been developed and summarized [14]. The 
ranges and modeling constants for four semiconductor wearout failure mechanisms and 
associated models are presented in Table 4. A detailed discussion on the modeling 
constants related to time dependent dielectric breakdown is shown in Chapter 3. 
Table 4: Sample semiconductor failure mechanisms and associated models 
Mechanism JEP122H Model [14] Constant Value Ranges 
Time Dependent 𝛾𝑉𝑔 𝐸𝑎𝑎 0 < 𝛾 < 2 
𝑇𝑇𝐹 = 𝐴0 exp (− ) exp ( ) 
Dielectric Breakdown 𝑡𝑜𝑥 𝑘𝑇𝑗𝑢𝑛𝑐 0.3 < 𝐸𝑎𝑎 < .6 
𝐸𝑎𝑎 2 < 𝑁 < 4 
Hot Carrier Injection 𝑇𝑇𝐹 = 𝐴 −𝑁0𝐼𝑠𝑢𝑏 exp ( ) 𝑘𝑇𝑗𝑢𝑛𝑐 −.2 < 𝐸𝑎𝑎 < .4 
∆𝑝: 𝑆ℎ𝑖𝑓𝑡 𝑖𝑛 𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 
1
Negative Bias ∆𝑝 𝐸 𝑛 3 < 𝛼 < 4 𝑎𝑎
Temperature Instability 𝑇𝑇𝐹 = [ exp ( ) 𝑉
𝛼
𝑔𝑒]  𝐴 𝐾𝑇 0.15 < 𝑛 < 0.25 0 𝑗
−.01 < 𝐸𝑎𝑎 < .15 
3000 7000
< 𝐽
𝑙 𝑐𝑟𝑖𝑡
<  
𝐸 𝑏
𝑙𝑏
𝑎𝑎
Electromigration 𝑇𝑇𝐹 = 𝐴0(𝐽 − 𝐽
−𝑛
𝑐𝑟𝑖𝑡) exp ( ) (𝑙𝑏) is length of gate 𝑘𝑇𝑗 𝑛~2 
0.5 < 𝐸𝑎𝑎 < 0.6 
17 
 
 
Chapter 3: Information Requirements for Modeling 
As explained in Chapter 2, the reliability of an electronic part is dependent on 
application conditions, part information, and modeling constants. Information related 
to each of these factors must be found (or approximated) for a proper reliability 
estimation to be made. As each input is treated as a distribution representing 
information uncertainty, the more information that can be found, the less uncertain the 
final to failure distribution will be. Each of three main input aspects is discussed below 
in the context of methods of collecting information and quantifying the uncertainty in 
the information.  
Application Conditions 
The reliability of a part is directly dependent on the application conditions in 
which the system is used and exposed too. The application conditions include 
environmental conditions such as temperature, humidity, and vibration, as well as 
operating parameters like voltage and current. As shown in the failure models from 
Table 4, temperature is key for estimating the time to failure, as well as other 
application parameters like threshold voltage or substrate current. Without knowing or 
approximating these values, the time to failure cannot be accurately determined.  
Operating condition limiting values are provided for a part in a datasheet, 
webpage, or other document. Depending on the type of part and manufacturer, this 
information can be provided as a single value or given with upper and/or lower limits. 
However, this information should be used for designing and integrating the part into 
18 
 
 
the system, not for estimating the application conditions and reliability of the part. The 
actual usage of the part will not identically match the value or range of values. 
Whenever possible and information available, the reliability of a part should be 
evaluated based off of the true application usage. The different levels of information 
collected for determining application condition distributions are as follows: 
1. Collect sensor information from actual application environment 
2. Approximate temperature range using past knowledge. 
3. Derated usage guidelines for a specific application and part 
4. Approximate using maximum ratings for a specific part 
Sensor Collected Information  
One method of determining the actual application usage and conditions is 
through sensor monitoring. Unlike with using the datasheet nominal value, this method 
represents the actual usage of the part and can capture additional aspects that a single 
value cannot. A part will not always be exposed to the maximum rated temperature of 
usage for the entirety of the life of the part. To show the difference on a small scale, 
processor temperature data was collected for 14 minutes during usage and compared 
with the maximum temperature provided in the datasheet (results shown in Figure 5). 
Even during high usage, the part does not reach, let alone remain, at the maximum 
temperature value. Thus, using the maximum value to determine an actual reliability 
estimation is not valid. Additionally, a part’s usage will depend on the requirements of 
the system and may not be powered or “turned on” at all times. Estimating the reliability 
19 
 
 
with a datasheet value will not effectively account for duty cycle operation or only 
partial usage.  
 
Figure 5: Processor temperature measured during usage compared with datasheet 
maximum value. 
The method by which sensor information is collected and for which attributes varies 
depending on the system and application. If available, time series sensory data can 
provide specific information for application conditions over a device’s lifecycle. For 
example, sensor information collected from cell phones is recorded either at period 
instances or a change in state with an associated timestamp [39].  
The process of converting individual measurements of parameters to a 
distribution which can be sampled for reliability distributions is completed using a 
kernel density function. The process is completed using the following steps: 
20 
 
 
1. Collect application condition information of interest over a certain length of 
time using sensors or other monitoring equipment. 
2. Using the values from step 1, a kernel density function is used to approximate 
the sample distribution in incremental distances.  
The kernel density function is dependent on the specific kernel that is used and 
a bandwidth parameter which controls the severity of the kernel. When a gaussian 
kernel is used, the bandwidth is the standard deviation that is put around each point in 
the dataset. Using the kernel density function method, the estimated density at any point 
x within the dataset X is shown in equation 7. 
𝑛
1 𝑥 − 𝑥𝑖
𝑓(𝑥) = ∑ 𝑲 ( ) 7 
𝑛 ℎ
𝑖=1
where K is the kernel function, n is the number of samples in the dataset, and h is the 
bandwidth parameter in the range of (0,1). A gaussian kernel is used with form shown 
in equation 8. 
1 1
𝑲(𝛼) = exp (− 𝛼2) 8 
√2𝜋 2
The bandwidth parameter must be selected for each dataset individually. From 
equation 7, a lower bandwidth value means that the differences between x and 𝑥𝑖 will 
be magnified and lead to a more complex, less smooth density estimation. If a high 
bandwidth value is selected, the differences between values will be smaller and a 
smoother function will be generated. Figure 6 shows a comparison of different 
bandwidth values for a gaussian kernel density on 2000 normally distributed values 
21 
 
 
with mean of 5 and standard deviation of 1. The blue line with h = 0.1 has a noisy 
function as it overfits to the individual samples, whereas h = 0.9 overly smooths the 
function and does not capture all of the underlying data.  
 
Figure 6: Comparison of different bandwidth (h) values on a gaussian kernel density 
function generated from 2000 samples with mean of 5 and standard deviation of 1. 
Depending on the assumed kernel, there are rules that have been developed for 
selecting bandwidth values. For a gaussian kernel, there are two primary rules for 
determining the bandwidth value: Scott’s Rule [40] and Silverman’s Rule [41] (the 
equations below show the formula for determining a bandwidth value with these rules 
assuming a single series of data). 
22 
 
 
1
𝑆𝑐𝑜𝑡𝑡′𝑠 𝑅𝑢𝑙𝑒:   ℎ = 𝑛−5 9 
1
3𝑛 −5
𝑆𝑖𝑙𝑣𝑒𝑟𝑚𝑎𝑛′𝑠 𝑅𝑢𝑙𝑒:    ( )  10 
4
In practice, the kernel density function is determined at incremental distances 
(K) over the space of the input samples. The smaller the incremental distance, the finer 
the control over where the final samples will be selected from. 200 different increments 
were selected for evaluating the input application condition information and the kernel 
density at any increment k is labeled as 𝑓𝑘(𝑥). 
3. Next, each kernel density value corresponding with each increment is converted 
into a Cumalitive distribution. The final increment will have a value of 1. The 
Cumalitive value at each increment k is provided in equation 11. The final value  
𝑘
𝐹𝑘(𝑥) =  ∑ 𝑓𝑗(𝑥) ∀𝑘 = 1 … 𝐾 11 
𝑗=1
4. Generate N uniformly random samples between [0,1] and determine which 
increment the random number falls in. The number of samples N determines 
how many samples will be used for the final time to failure distribution and 
should be the same for all of the inputs. Selecting which increment each random 
sample belongs to can be determined by finding the next increment value higher 
than the random sample value.  
5. The selected increment’s corresponding value is the final output sample value. 
A visual representation of the conversion process is shown in Figure 7.  
23 
 
 
 
Figure 7: Process for converting input samples to output samples through 
distribution approximation. a) provides (randomly generated) temperature samples, 
b) shows the kernel distribution estimation and corresponding bins, c) converts the 
distribution into a cumulative form and shows randomly generated points between 
[0,1] and the corresponding bins that they fall in, d) shows the final sampled values 
compared with the kernel distribution. 
24 
 
 
To compare different kernels and bandwidth values on the distribution 
approximation methodology, temperature data was collected from a laptop processor 
(Intel I7-8550U) over 1400 seconds during normal usage. Figure 8 shows the time 
series temperature data that was collected.  
 
Figure 8: Collected temperature sample readings from Intel I7-8550U processor. 
Using this information, the impact of the kernel bandwidth was evaluated. A 
guassian kernel was selected and the temperature range was split into single degree 
increments between the minimum and maximum value to match the precision of the 
temperature monitoring software. The resulting kernel distributions generated for 
different bandwidth values are shown in Figure 9. As expected, with a lower kernel 
bandwidth value the distribution is much more sensitive to changes. This leads to the 
situation in which the distribution is drastically dropping in between each discrete 
25 
 
 
measurement value which is not representative of the true application. As the kernel 
bandwidth value is increased, the kernel more closely represents the true distribution 
and then starts to over-generalize or smooth at high values (black line with bandwidth 
equal to 1).  
 
Figure 9: Comparison of different kernel bandwidths for approximating temperature 
distribution. Input samples histogram converted to a discrete probability distribution. 
Additionally, analysis was completed to evaluate different kernels other than 
the gaussian kernel. Using the same collected temperature data a gaussian, exponential, 
and Epanechnikov kernel were selected based on their frequency of use in completing 
density approximation methods. For each case, the bandwidth was held as a constant 
at 0.5 and the results are shown in Figure 10.  
 
26 
 
 
 
Figure 10: Comparison of different kernels for approximating a sample temperature 
distribution.  
Derating Conditions Approximation Method 
In many cases, collecting specific application data is not possible or efficient. 
For example, monitoring threshold voltage for individual transistors may not be 
possible or convenient. Estimating application conditions without a known profile or 
sensor information can be completed using standards and guidelines for specific 
applications. For example, NASA publishes derating guidelines for device parameters 
such as temperature, power dissipation, and voltage [42]. Example derating guidelines 
are shown in Table 5.  
Table 5: Derating guidelines for transistors provided by NASA [42] 
Stress Parameter Derating Factor 
27 
 
 
Power 0.60 
Current 0.75 
Voltage 0.75 
Junction Temperature* 0.80 
*Do not exceed Tj = 125 °C or 40 °C below the datasheet maximum rating. 
Applying derating guidelines must be done considering the meaning of the 
parameter and the functionality of the part. For example, the same derating standard 
applies a derating guideline of 0.8 for power MOSFET gate voltage [42]. In theory, if 
the gate voltage drops below the minimum threshold value, the device will not turn on 
and the part will not function as intended. Utilize the part information before making 
any judgements with derating guidelines. As seen previously, the threshold voltage is 
also known to change with temperature and thus should also be considered when 
selecting a derating value [43]. 
The derating guideline limit is the upper limit on the application stress condition 
and is modeled by selecting a distribution with the same maximum value. This is like 
the situation in which only the part’s maximum ratings are used. Selecting the form and 
values for the distribution depends on the application that the part is used in and will 
directly impact the reliability of the part. An application that is frequently near the 
upper derated limit or part rating will have a different distribution than a part in an 
environment which never approaches them. For example, PLC sensor circuity used 
inside a controlled environment manufacturing line may never reach the part or 
derating limits. However, a similar PLC sensor mounted outside on an amusement park 
ride may experience extreme temperature and vibrations near the derating or part limits. 
28 
 
 
The distribution for modeling the temperature of these applications is completely 
different.  
A summary comparison of the different application condition methods is shown 
in Table 6. The table is sorted based on the quality in which the application condition 
will be modeled to accurately represent the true usage conditions.  
Table 6: Comparison of application condition collection methods 
Approximation 
Advantages Disadvantages 
Method 
Time Series • Most specific information • Requires installation of sensors 
• Best representation of actual 
Data Collection and collection of information 
application 
• Not as accurate modeling 
Previous • Quick implementation which • Requires selecting distribution 
Application can adapt over time as more form and attribute values 
Experience experience is gained 
 
• Specific values provided in 
• Not available for all applications 
standards 
Derated or types of parts 
• Does not require any additional 
Guideline • Requires selecting distribution hardware on systems to collect 
Limitations form and attribute values information 
 
 
• Is not related to the application 
Part Maximum • Provided for almost every part and will not give reliability 
Ratings estimations related to actual usage.  
 
Part Information Sources 
The information that is available for a part depends on the type of part itself, the rating 
to which it is  
29 
 
 
Commercial Sources 
Finding the part information for reliability assessment and modeling requires 
locating and analyzing many different documents. Traditionally, the datasheet is the 
primary document that is used to share information about a part, but a datasheet alone 
will not provide all the information needed. For all parts, many different documents are 
available that can be used for reliability modeling. A list of common documents 
provided and the types of information that can be found is provided in Table 7.  
Table 7: Summary of information sources for COTS electronic parts 
Data Source Example 
Data Source Applicable Information 
Type Sources 
• Part Ratings (Threshold Voltage / 
Maximum Substrate Current) 
Datasheet [44], [45] 
• Environmental Ratings 
(Temperature / Humidity Ratings) 
Qualification • Part Dimensions 
[46] 
Report • Testing Levels / Requirements 
Product Change • Material Composition 
[47] 
Notification • Part Structure / Packaging 
Application 
• Expected Failure Mechanisms [48] 
Note 
Manufacturer 
• Reliability Report Data and 
Reliability [28] 
qualification levels 
Testing 
• Material Information, Qualification 
Industry 
Testing Levels, Application Limits [42], [49] 
Standards 
and Conditions 
• Model Parameters 
Research Papers [30]–[38] 
• Activation Energy Information 
 
30 
 
 
Other Source Manufacturer Data Source 
The documents described in Table 7 will not be available for all COTS devices. 
This is one of the main restrictions of COTS devices as the consistency of information 
is not guaranteed. Alternatively, all non-COTS devices (such as military, space, or 
automotive qualified parts) should have the same standardized tests, requirements, and 
even information format. There is specific documentation associated with parts that are 
automotive, space, or military qualified [50], though the information within these can 
be found for COTS parts in some cases. A summary of the information that can be 
found from each commercial source is discussed in each of the sections below.  
Datasheet 
The classical document used for gaining part information is the part datasheet. 
The part datasheet outlines the performance parameters, operating conditions, physical 
dimensions, and other aspects depending on the type of part. Every part or family of 
parts will have a datasheet. Each datasheet typically includes the following sections: 
introduction, absolute maximum ratings, electrical specifications, part layout, contact 
information, and document updates. These sections will vary in name and order 
depending on the manufacturer, but these sections at minimum should be included in 
an effective datasheet. When compared to previous reports on part datasheets, 
datasheets now rarely include testing or quality data sections as these are in their own 
documents [51].  
The introduction is the first section that provide a summary of the part. This 
includes the part number, which describes the specific part in question. Figure 11 shows 
the information provided through the part number for an Intel processor [52]. The 
31 
 
 
introduction will also include a basic description of the part, as well as the specific use 
or applications that the part can function in. 
 
Figure 11: Information provided within the part number for an Intel processor [52]. 
The absolute maximum ratings provide the limiting values for the part. Analog 
Devices describes these ratings as “parameters that must not be exceeded [53].” These 
parameters vary depending on the type of part being used, but factors such as operating 
and storage temperature range, maximum power dissipation, thermal resistance, and 
some voltage and current limits will typically be included. Most datasheet includes a 
comment below the absolute maximum ratings warning that these are “stress-based” 
ratings and that exceeding these ratings can result in immediate part failure. These 
specifications are the maximum ratings that can be used as a worse case scenario when 
modeling application condition distributions. 
The recommended or electrical specifications provide the values for the key 
parameters of the device. The range of these values is where the performance of the 
part is guaranteed. As long as the system parameters do not exceed what is listed in this 
section, the system should perform properly and not experience immediate reliability 
concerns (such as overstress). This can also include charts that determine how one 
32 
 
 
parameter is impacted by another parameter, such as temperature [43]. This information 
is useful for design but can also be used for part parameters.  
 
Figure 12: Sample curve of the impact on turn on voltage with respect to temperature 
[43]. 
Part Webpage 
The part webpage serves as an introduction to the part and gateway for more 
detailed information through downloadable documents and other linked pages. Each 
part manufacturer has their own style of part information page which will vary but are 
usually consistent within a single manufacturer. The page traditionally feature at least 
a link to the datasheet, some basic ratings and features, a set of documents associated 
with the part, and an image of the part. Vishay Siliconix (part SIS415DNT) has specific 
sections on specifications, documents, design tools, quality, and a place to request 
samples or ask questions [15]. Texas Instruments provides similar information for part 
CSD17318Q2 but also includes the status (active vs. obsolete) and similar parts [55]. 
33 
 
 
Unlike with datasheets or other .pdf files, part information webpages are easily 
searchable and allow for compilation of information quickly.  
Qualification Report 
The qualification report for a specific part provides more detailed information 
about the part, specifically including information from different tests that have been 
completed on the part. This testing can include thermal, electrical, and physical testing 
and characterization of the part that is completed by the manufacturer [56]. In addition 
to testing results, more rigorous material composition of the packaging and die structure 
can be provided. While very useful, qualification reports are not provided for all parts 
within a company, and thus cannot be used as a reliable method for collecting 
information. 
Application Notes 
Application notes provide specific insight by the manufacturer for usage of 
parts in a specific application. This can include how to integrate the part into a specific 
circuit, mount the device properly, or understand the thermal properties of a device. 
Application notes can be part specific or related to families of parts. A web scraping 
analysis was completed based on the Vishay and ON Semi technical libraries, which 
contains application and technical notes covering their products. The pages feature a 
table of application note files across all types of parts. By analyzing the title string for 
each document, the information content can be determined. Table 8 shows the most 
frequently found words in the titles of the strings for both manufacturers. The most 
common term was “Power ” for both manufacturers. There are also several different 
34 
 
 
part types such as MSOFET, Resistor, and Capacitor that frequently have application 
notes published. Others include terms like “Thermal” or “Mounting” which give ideas 
about the content of the actual application notes. 
Table 8: Most common terms and their frequency of occurrence in Vishay and ON 
Semi Technical Libraries 
Vishay (285 Notes) ON Semi (1426 Notes) 
Percentage of Percentage of 
Term Term 
Notes (%) Notes (%) 
Power 16.84 Power 14.31 
Resistors 11.23 Design 9.33 
MOSFET 9.82 Driver 7.57 
Mounting 9.82 Converter 6.03 
Instructions 8.07 Board 5.75 
Capacitors 6.67 Evaluation 4.42 
Film 6.32 Motor 3.86 
Converter 4.91 High 3.79 
Voltage 4.56 MOSFET 3.72 
Thermal 4.56 Supply 3.58 
Modules 4.21 Voltage 3.44 
Guidelines 3.86 Series 3.09 
 
The titles of the application notes from both manufacturers show that certain 
aspects like Power and MOSFET are frequently discussed. Vishay notes tend to have 
more part type specific notes (with terms like Capacitor, Resistor, Module) then ON 
Semi. The most common term for both part manufacturers was Power and may of the 
notes were related to power management solutions.  
Product Change Notifications (PCNs) 
Product Change Notifications (PCNs) are documents issued by the 
manufacturer that detail any change in the construction, operation, or capabilities of the 
35 
 
 
device. PCNs can provide information regarding a change in manufacturing location, a 
change in material composition, or an altering in the expected performance parameters 
for the part due to updated testing or other changes. Unlike for datasheets or 
qualification reports, PCNs will typically be for a range of products provided by the 
manufacturer, and not an individual part. At a bare minimum, a PCN must include a 
unique code or number for identification, a definition or classification of the proposed 
part changes, the timing for when the change will occur, the deliverables to the 
customer, and record retention requirements [57]. PCNs can be utilized in the part 
selection process for both initial selection and long-term considerations. The initial 
selection process can require information that can only be found in a PCN for the part, 
and long-term evaluation for monitoring if the part still maintains the required 
performance levels for the application. For example, a PCN released by Altera reports 
on the changing of both the epoxy mold compound and bond wire material for specific 
BGA packages [58].  
Commercial Part Information Templates 
Templates have been developed to allow for the entry of information based on 
the requirements for specific failure mechanisms. Each template is based off a transistor 
(MOSFET or IGBT) and is split into aspects based on part parameters and application 
information. As an example, the template part and application condition information 
requirements are provided in Figure 13 and Figure 14 respectively.  
36 
 
 
 
Figure 13: Part information required for failure mechanism template (TDDB) 
The part information required for the template is the combination of part 
material and geometric features, datasheet parameters, and modeling constants. By 
using part specific features, the reliability estimations are also part specific. For the 
TDDB case, the only geometric feature is the oxide layer thickness of the device. The 
other datasheet parameters can be used for estimation of other parameters in multiple 
methods. One method is to use these values as approximations for unknown application 
information. An example of this is using the maximum power dissipation for the device 
to approximate the actual power dissipation the part will experience. Another method 
is to use relate information about this part to other similar parts. Then, any unknown 
information from the original part can be approximated using information from similar 
parts. This assumes that parts with similar information and design will have similar 
reliability if all else is consistent. 
37 
 
 
 
Figure 14: Application condition information for failure mechanism template 
The application information portion of the template is designed to allow the 
entry of information over a period or cyclic fashion. This will allow for a much better 
representation of the application environment and thus reliability estimations. In the 
example of TDDB (see Figure 14), the “Gate-Emitter Voltage” column is used for 
determining the electric field parameter in the model and the “Temperature” column is 
used for the temperature parameter. The final two columns are used for determining 
the actual power dissipation of the device. These columns would be different for 
different device types. At each increment of time, this information can be entered to 
form a distribution around the parameters. 
Node Size Approximation Method 
When information is not provided or cannot be found, other methods have to 
be used to determine the input distributions. Approximation of part information can be 
completed using the device node (or feature) size. The node size is the minimum 
38 
 
 
channel length of a transistor within a processor or other device. This is typically 
provided in relation with the description of a processor (such as a 7 nm technology), 
although the name for a processor does not necessarily represent the actual node size 
for the part [59]. The node size is associated with Moore’s law which described the 
doubling of the number of transistors (and thus reduction in transistor size by 2) each 
year. Figure 15 shows the most recently developed node size each year frm 1970.  
 
Figure 15: Change in most currently developed node size in each year. 
Because many of the required properties for failure mechanism models are 
geometric, the node size can be used to determine an approximation or range on the 
value. This includes properties like the gate height and gate oxide layer thickness which 
are properties needed for failure models and cannot be easily found. By analyzing 
reports from device manufacturers, the change in these properties in relation to node 
size has been completed (see Figure 16 for an example based on the gate oxide 
thickness layer).  
39 
 
 
 
Figure 16: Change in oxide layer thickness in relation to node size. 
Uncertainty is introduced when the approximation method is used for properties 
by approximating a normal distribution based on the known values from the technology 
reports. This means that a part with a known oxide thickness will have less variation in 
the input when compared to a part where the oxide thickness is unknown and is 
approximated using the node size. This follows the same basic principle that when more 
specific information is known, the level of uncertainty is reduced. For this process, it 
is assumed that the node size is based off of the smallest node size on the die in the 
instance where multiple different sized transistors are used.  
Higher Grade Part Information 
Automotive parts that meet the qualification requirements of AEC (Automotive 
Electronic Council) or space parts qualified to SAE AS9145 must complete a 
40 
 
 
production part approval process (PPAP) [49], [60]. The PPAP documentation 
originally started with the automotive industry but has moved to space parts [61]. This 
process requires documenting of the design, manufacture, and status of a part to the 
customer. Each PPAP document contains 18 – 20 sections including material 
information, qualification testing results, and design / process failure mode effect 
analysis [49], [62]. This information is useful for comparing parts and can be used to 
better understand the expected reliability of the part. This is a prime example of 
information that is expected for non-COTS parts but will not be found for COTS parts.  
The availability of PPAP documentation varies for parts and manufacturers. 
This was evaluated by analyzing all of the MOSFETs provided on the Diodes Inc. 
website [63]. In total, Diodes Inc. has 1174 MOSFETs, 179 of which are rated as 
commercial (COTS) and the remaining 995 are automotive parts. Figure 17 shows the 
results of the analysis. Of the automotive parts, 19% do not provide a PPAP document, 
48% provide a PPAP document with an additional request, and the rest have a direct 
link to the PPAP document. None of the 179 COTS MOSFETs have a PPAP document 
associated with them.  
41 
 
 
 
Figure 17: Availability of PPAP documentation for Diodes Inc. MOSFETs 
A PPAP document provides a consolidation of information from a sole source 
that cannot be found for COTS products; however, some of the information found in 
this document is correlated with documents that can be found for COTS devices. For 
example, one PPAP section requires qualification test results which can also be found 
through a qualification testing report [46], although the same level of analysis is not 
completed. This shows that, while not as convenient as a PPAP, other documents can 
be used to find similar levels of information.  
The current method by which military-grade parts are released by part 
manufacturers is through qualification with MIL-PRF-38535. MIL-PRF-38535 has 
different qualification requirements dependent on the application requirements or type 
of part which are designated by different QML (qualified manufacturer list) classes 
[64]. The standard was developed as a replacement for the Qualified Products List 
(QPL). Under QPL, individual part designs had to meet specific qualifications. QML 
is instead based on qualification of specific production lines and designs by specific 
42 
 
 
manufacturers. Overall, this resulted in lower total qualification time in a hope to 
increase the usage by part manufacturers. Table 9 displays the different QML 
qualification levels (with classes lower in the table corresponding to higher 
qualification requirements).  
Table 9: MIL-PRF-38535 QML Class and Descriptions 
QML Class Specification 
M Vendor Self-Verification Parts 
N Plastic Parts 
Q Hermetic Parts 
Radiation-Qualified Hermetic 
V 
Parts 
 
The QML qualification class is critical for evaluating a part, and just assuming 
that a part that is MIL-PRF-38535 qualified will have the expected reliability and 
performance is incorrect. NASA only considers QML Class V parts to be “low risk” 
for space applications, and considers classes M, N, and T to be “high-risk” parts [65]. 
Depending on the qualification class, different testing and reporting 
requirements must be met. Many tests are based off of industry standards or use test 
methods from MIL-STD-883. MIL-STD-883 provides test methods for standard 
microelectronic devices. Table 10 shows example test methods that are used to qualify 
electronic parts for specific tests.  
43 
 
 
Table 10: Example standards for different military test qualifications 
 
Modeling Constants 
Modeling constants are needed to make failure models generalizable for 
different parts or usage conditions, and each part will have specific constants. The best-
case scenario is when these specific constants are provided for a part. This situation is 
44 
 
 
unlikely to occur, and thus other methods must be developed to estimate or determine 
them. One solution is to complete a set of experiments with varying environmental 
conditions and part parameters to determine the modeling constants for a specific part. 
This process is not usable when dealing with many different parts within a system due 
to the time and cost requirements associated with physical testing.  
Another method is to evaluate modeling constants by analyzing the results 
information provided within research papers. This process must be completed based on 
a specific failure mechanism (and thus failure model). Instead of completing tests 
separately, the modeling constants are determined by completing an optimization 
problem to fit the failure model to the data found in a research paper. Part parameters 
and application condition information are taken from the documents and used as the 
inputs to the optimization problem. Table 11 shows sample information collected from 
research papers related to the TDDB failure mechanism with each shaded region 
representing a different part that analysis was completed on.  
Table 11: TDDB Time to failure data collected from research papers for TDDB (each 
region are results from a different part). 
Vg Tox 𝐸𝑜𝑥 Temp 
TTF (s) 𝑀𝑊
(V) (nm) ( ) (K) 
𝑐𝑚
1932.78 3.78 2.00 18.92 300 
17394.41 3.63 2.00 18.13 300 
156000 3.44 2.00 17.19 300 
3159.11 4.51 3.00 15.02 300 
278.59 4.74 3.00 15.80 300 
21.50 4.98 3.00 16.60 300 
200.99 4.96 3.40 14.58 300 
22.40 5.20 3.40 15.29 300 
45 
 
 
Vg Tox 𝐸𝑜𝑥 Temp 
TTF (s) 𝑀𝑊
(V) (nm) ( ) (K) 
𝑐𝑚
14994.29 3.21 1.40 22.95 300 
2448.44 3.31 1.40 23.63 300 
118.60 3.51 1.40 25.04 300 
29.04 3.60 1.40 25.75 300 
1.56 3.81 1.40 27.20 300 
0.06 4.00 1.40 28.57 300 
 
Modeling was completed on a per part basis using linear least squares 
optimization. For the example of TDDB, the optimization takes on the form of equation 
12. The minimization was completed using the lmfit software package within Python. 
The optimized model constant values were then used to predict the time to failure as 
validation. Figure 18 shows the final projected time to failure for one part compared 
with the actual time to failure.  
𝑛 2
1 𝛾𝑉𝑔 𝐸𝑎𝑎
min 𝜖(𝐴0, 𝛾) = ∑ (𝑇𝑇𝐹𝑖 − 𝐴0 𝑒𝑥𝑝 ( ) exp ( ))  
A0,𝛾 2 𝑡𝑜𝑥 𝑘𝑇𝑗
𝑖=1 12 
 
46 
 
 
 
Figure 18: Predicted vs actual time to failure using optimized model constant values.  
Time Dependent Dielectric Breakdown Modeling Constant Analysis 
The electric field for the part can be found by dividing the part operating voltage 
by the oxide layer thickness. Sample values for the operating voltage, oxide thickness, 
and subsequent electric field are shown in Table 12. This information was found from 
multiple technical documents published by intel for each new part node size [33].  
Table 12: Impact of Node Size on Electric Field Parameters [33] 
𝑴𝑽
Node Size 𝒕𝒐𝒙 (nm) 𝑽𝒄𝒐𝒎𝒑 (V) 𝑬𝒐𝒙 ( ) 𝒄𝒎
350 nm 6.9 – 8.1 3.6 4 – 6 
180 nm 3.5 1.8 5 
130 nm 2.2 1.2 – 1.5 5 – 7 
90 nm 1.2 1 - 1.2 8 – 10 
65 nm 1.2 - 1.6 1 8 – 10 
45 nm 1 1.1 10 – 15 
20 nm 1.1 0.9 8 – 11 
7 nm 0.85 0.7 8 – 12 
47 
 
 
 
As seen in Table 12, the electric field increases with decreasing node size. 
Based off the thermo–mechanical model, the expected time to failure will decrease with 
increasing electric field, and thus TDDB wearout becomes a larger concern as smaller 
node size parts are implemented. In addition to the electric field, the relation of electric 
field and activation energy has been analyzed by correlating the activation energy with 
the effective dipole moment and enthalpy of formation for the 𝑆𝑖𝑂2 bonds in question 
(13).  
𝐸𝑎𝑎 = (∆𝐻)𝑜 − 𝑎𝐸𝑜𝑥 (13) 
where 𝐸𝑎𝑎 is the apparent activation energy for TDDB, (∆𝐻)𝑜 is the enthalpy of 
activation for bond breakage, a is the effective dipole moment for the bond breaking, 
and 𝐸𝑜𝑥 is the externally applied electric field. 
Based on the energy level for the 𝑆𝑖𝑂2 bond in question, which correspond to 
specific electric field ranges, there are values for the effective dipole moment and 
enthalpy of formation required to break the bond. These values, along with the specific 
electric field for the part in question, can be used to determine the activation energy for 
the part [38]. Table 13 shows the resultant values and usable electrical field range for 
the low and high energy levels. Figure 19 shows the two different energy levels and 
corresponding impact on activation energy, as well as the transition period between the 
two [38]. The activation energy has also been directly related to the node size of the 
part, as seen in Figure 20 [38].  
 
48 
 
 
Table 13: Modeling Parameters for activation energy [38]. 
Usable Electric Field 
Energy Level 𝑴𝑽 𝜶 (𝒆?̇?)  ∆𝑯𝟎 (eV) 
Range ( ) 
𝒄𝒎
Lower 9 – 13 (and Higher) 13 1.95 
Higher 3 – 5 7.4 1.3 
 
 
Figure 19: Relation of activation energy and electric field over two different bond 
energy levels. 
 
  
Figure 20: Relationship of activation energy and node size 
49 
 
 
The relationship between the electric field and gamma (field acceleration 
parameter) has also been analyzed. The equation used for determining the effective 
gamma parameter is shown below [38]. The same alpha values apply for correlating 
the first two levels of energy in bond breaking. Figure 21 shows the two different 
energy level models for different electric fields and relates the gamma parameter and 
part temperature.  
𝛼𝑚
𝛾𝑒𝑓𝑓 =  (14) 𝑘𝐵𝑇
Table 14: Usable temperature range and corresponding 𝛼 value for different energy 
levels [38]. 
Energy Level Usable Temperature Range (𝑲) 𝜶 (𝒆?̇?)  
Lower 600 - 1000 13 
Higher 0 – 200 7.4 
 
 
Figure 21: Relation of gamma parameter and temperature over different electric 
fields and energy levels [38]. 
50 
 
 
Suehle and Chaparala also analyzed the relationship between the gamma 
parameter and the applied temperature as well as adding the oxide thickness level as 
another parameter [66]. Figure 22 shows the results from this study. This result seems 
to contradict the result found in Figure 21. With this study, there does not seem to be a 
definitive relationship between the gamma parameter and the part temperature, whereas 
a trend does exist for [38]. This discrepancy may be explained by the temperature 
ranges that were used during testing. In [66], the range of temperatures aligns with the 
transitional period found in [38] where neither of the two energy level models aligns 
with the resultant gamma parameter value.  
 
Figure 22: Relation of gamma parameter, temperature, and oxide layer thickness.   
 
51 
 
 
Chapter 4: Information Availability Metrics 
Determining the consistency and quality of information provided by part 
manufacturers is a key aspect for evaluating part level reliability. If information is not 
available, assumptions must be selected which can lead to more uncertainty in 
reliability projections. A sample part from four different part categories (all from 
Vishay) were analyzed based on the types of documents that were provided (and thus 
different information provided). The results of this analysis are shown in Table 15. 
Compared with the other parts, the information associated with the MOSFET was the 
highest. In all cases, different documentation and information were provided. The only 
document and associated information provided in at least 3 of the parts was the 
datasheet.   
Table 15: Comparison of Information Provided for Vishay COTS Parts 
Part Type MOSFET LED Optocoupler Thyristor 
• Datasheet • Datasheet • Datasheet • Datasheet 
• Markings • 3D Models • Application 
• Package • Application Note 
Drawing Note • Package 
• Pad • Certificates Drawings 
Guidelines 
• Thermal 
Models 
• Reliability 
Data 
• Tape Info 
• Tech Tips 
• SPICE 
Models 
 
52 
 
 
Provided Information 
Additionally, a web scraping algorithm was used to evaluate the consistency of 
information for MOSFETs manufactured by Infineon. The information for 1410 
MOSFETs from Infineon was collected from the searchable spreadsheet on the 
Infineon webpage [67]. A summary of the availability of information for the MOSFETs 
based on key parameters that define the part and are related to the reliability is shown 
in Table 16.  
Table 16: Information Availability for Parameters from Infineon MOSFETs Part 
Selection Table 
Percentage of Parts 
Category 
(1410) 
Minimum Temperature 36.80% 
Maximum Temperature 36.50% 
Power Dissipation 88.10% 
Drain-Source Voltage 99.90% 
Thermal Resistance 21.90% 
Gate Voltage 11.10% 
Technology (node size) 98.10% 
Package Type 100% 
 
The device technology, package type, and drain source voltage were found for 
almost every MOSFET. Power dissipation values were found for 90% of parts while 
thermal resistance values were found for only 20% of parts. The most interesting result 
was that temperature was only provided for 36% of the parts and gate-source voltage 
was only listed for 11% of samples in the searchable database. Because this process 
was collected in an autonomous fashion in a searchable database, some of the missing 
information may be on the individual part pages or within documents. A more thorough 
53 
 
 
algorithm that collects from each individual page may produce different information 
availability results.  
Metrics have been developed to evaluate the information availability provided 
by manufacturers, for part types, and for specific parts. These metrics can be used for 
evaluation of manufacturers and incorporated into failure time estimation. The 
development of these metrics is completed based off of information that is readily 
available by manufacturers on the part webpage, but can be updated and expanded 
based on additional information collection methods and contact with the manufacturer.  
Thermal Information Availability (TIA) 
Thermal information is needed for determining if the part can meet the 
application requirements of the final system. The primary thermal information 
associated with a part is the operating temperature range, storage temperature range, 
thermal resistance, and power dissipation. The thermal information availability (TIA) 
metric is based on evaluating how much of the above information is provided for a 
specific part. This metric has been designed as the product of three specific multipliers 
and is based on a scale between 0 and 1 (metric form is provided in equation 15). The 
best possible rating is 1 where specific absolute, recommended, and storage 
temperature ratings and associated locations are provided, as well as power dissipation 
and thermal resistance conversion parameters. A metric result of 0 is obtained if no 
temperature ratings are provided for the part.  
54 
 
 
𝑇𝐼𝐴𝑝𝑎𝑟𝑡 = (𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛)(𝑃𝑑𝑖𝑠𝑠 & 𝑅𝑡ℎ𝑒𝑟𝑚)(𝑅𝑎𝑡𝑖𝑛𝑔𝑠) 15 
Initial determination of these values for a part is based off of the part datasheet 
but can be changed depending on additional information that is found for the part, such 
as through communication with the part manufacturer or through analysis of research 
papers. The multiplier factor levels are determined subjectively and a process for 
continued evaluation and adjustment is provided at the end of the metrics section.  
Table 17: Location multiplier levels 
Location Description Multiplier 
Specific Location 1.0 
“Operating” or “Specified” 0.2 
No Description 0.01 
 
Table 18: Thermal resistance & power dissipation levels 
Power Thermal 
Dissipation Resistance Multiplier 
Provided Provided 
* * 1.0 
 * 0.8 
*  0.5 
  0.1 
 
Table 19: Temperature rating multiplier levels 
Absolute Recommended Storage 
Multiplier 
Temp. Rating Temp. Rating Temp. Rating 
* * * 1.0 
* *  0.9 
*  * 0.8 
 * * .75 
*   .6 
 *  .5 
  * 0.1 
   0 
 
55 
 
 
Table 17 provides the multiplier values based on the temperature location 
information provided in for the part. The best result for this multiplier is a specific 
location, such as junction, ambient, or case (see Figure 23 for relative locations on part). 
By providing this information, there is true meaning behind the temperature rating and 
it can be compared with other parts or converted to other locations within the part. 
Providing this information is rewarded with a high multiplier value. The second level 
is when only an “operating” or “specified” term is listed with the temperature rating. 
This results in a much lower multiplier factor because neither of these terms provide 
an identifiable location on the part. The worst multiplier level is when no location 
identifier is specified, and thus the multiplier value is the lowest possible value. This 
level of granularity was selected, but further details can and should be provided. If a 
case temperature is provided, detailing how and where on the part the case temperature 
applies is more informative than simply stating case temperature. In a similar fashion, 
an ambient temperature rating without a qualifying factor on how the measurement was 
taken is less valuable than one in which a specific distance from the part where the 
temperature was monitored is provided.  
 
Figure 23: Common temperature measurement locations in a part. 
56 
 
 
Table 18 provides the multiplier levels for the power dissipation (𝑃𝑑𝑖𝑠𝑠) and 
thermal resistance (𝑅𝑡) conversion information availability. This information is needed 
for completing the thermal design of the system and converting the temperature rating 
to different locations on the part. A common thermal resistance value is the conversion 
between the junction and ambient temperature value. This method is normally used for 
approximating the junction temperature from an ambient temperature, total power 
dissipation, and thermal resistance value [68]. 
𝑇𝑗 = R𝑡𝑃𝑑𝑖𝑠𝑠 + 𝑇𝑎 16 
The top multiplier level is when both the power dissipation and thermal 
resistance values are provided. The next best level is when only a thermal resistance 
value is provided. While knowing the maximum power dissipation is preferred, the 
power dissipation can also be determined using other parameters of the device and 
application. The next best case is when only a power dissipation values is provided. 
Without the thermal resistance parameter, the temperature conversion between 
different locations on the part cannot be completed. The worst case scenario is when 
no power dissipation or thermal resistances values are provided. 
The final multiplier factor is the actual temperature ratings themselves (shown 
in Table 19). The value of this metric is based off of the number of different ratings 
provided in the part datasheet, or other documentation. The three ratings included are 
absolute, recommended, and storage temperature ranges. The best possible multiplier 
value occurs when specific ratings for all three are given, allowing the user to 
understand the application limits for storage, normal usage, and absolute maximum 
57 
 
 
usage. As less information, or less detailed information is provided, the metric 
multiplier value decreases. Preference is given to absolute maximum ratings as those 
are the most common temperature ratings to be provided, and thus it is heavily 
penalized if this rating is missing. At this level the temperature rating values themselves 
are not impactful on the TIA value, though situations can arise where this would need 
to be further evaluated. For example, thermal uprating of parts is completed between 
the recommended and absolute temperature ratings for a part. If the recommended and 
absolute temperature rating are the same value, thermal uprating is not possible using 
the currently developed methods and reduces the value of the information. 
The current limitation with the metric is that it is fundamentally based on just 
the availability of the information and is not evaluating the information itself beyond 
the location parameter. This means the metric does not consider a case where over-
specification of parameters is provided, like when the maximum temperature rating, 
maximum power dissipation, and thermal resistance values do not correctly align. 
Additionally, the metric currently does not evaluate if the information’s accuracy. A 
manufacturer can provide information without completing validation or analysis to 
verify it. This can be addressed in future implementations by including additional 
information such as qualification testing to validate the information itself.  
Material Information Availability (MIA) 
Like thermal information, material information is also needed for evaluating 
parts and manufacturers. This information can be used for identifying bond wire 
58 
 
 
material and determining mold compound or die attach composition. The material 
information availability (MIA) metric is based on evaluating the ease with which 
material declaration information can be found for a part. IPC 1752 is a standardized 
format provided for sharing material information between the part manufacturer and 
the user. The format was designed to be flexible and supports several types of parts 
[69]. The standard format provides specific elemental composition, Chemical Abstracts 
Service (CAS) numbers, and weight percentages for each part aspect such as the die, 
lead frame, or encapsulant. It also features additional information like RoHS status and 
moisture sensitivity level (MSL). Figure 24 shows a sample IPC 1752 document for a 
MOSFET from ON Semi [70].  
 
Figure 24:Sample IPC 1752 document for MOSFET [70]. 
The MIA metric was designed to evaluate how easy it is to access material 
information. Many manufacturer websites require additional work like direct 
communication or account creation before access to specific documents can be 
completed [71]. Ideally, this information should be available in the part datasheet or on 
the part information page. The quality of the information presented must also be 
considered during the evaluation process. More specific or detailed material 
information affords a better representation of the part and improves the analysis and 
understanding of the part. Based off these factors, the metric has the following form. 
59 
 
 
The multiplier levels for the access and content factors are presented in Table 20 and 
Table 21 respectively. The MIA metric is also based on a scale between 0 and 1, where 
1 represents the best material information availability. 
𝑀𝐼𝐴𝑝𝑎𝑟𝑡 = (𝐴𝑐𝑐𝑒𝑠𝑠)(𝐶𝑜𝑛𝑡𝑒𝑛𝑡) 17 
Table 20: Access multiplier levels 
Access Description Multiplier 
Available on part information page 1.0 
Available on reliability or another searchable 
0.8 
page 
In datasheet or another document 0.6 
Requires account creation 0.5 
Requires email or other manual contact 0.2 
No access 0 
 
Table 21: Content multiplier levels 
Content Description Multiplier 
Official IPC 1752 document format 1.0 
Material information presented in table (not 
0.9 
IPC 1752 format) 
Specific RoHS document or detailed non-table 
0.3 
information 
RoHS symbol 0.1 
No Information 0 
 
As previously discussed, the access multiplier evaluates how easily material 
information can be found for parts from a manufacturer. The best-case scenario and 
highest multiplier level is when the information or document link is found directly on 
the part page. The next best level is when the information is on a reliability page where 
specific part numbers can be searched for. Both methods do not require the effort of 
making an account or having to contact technical support and thus receive higher 
60 
 
 
multiplier levels. The most heavily penalized case is when a direct email or technical 
form must be completed. This method does not guarantee getting any material 
information and will take a much longer time. Due to these factors, the MIA value for 
a part requiring an email is heavily penalized.  
For the content multiplier, the highest value occurs when the IPC 1752 official 
format is used. This can be in any file format that is supported by the standard, such as 
.xml, .csv, or .pdf. A 0.1 reduction in value is applied when specific material 
information is applied but it is not in the official IPC 1752 format. A much higher 
penalty is applied when non-tabular information is supplied, such as RoHS compliance, 
without specific elemental compositions. The worst case is when there is no material 
information available for the part, in which case the multiplier level and MIA value 
overall are 0. 
Metrics Value Usage 
Both metrics are evaluated on a per part basis and can be used for reliability 
estimation at a part level, comparison of individual parts, or generalized for evaluation 
and comparison of different part manufacturers. The sections below will describe how 
the metric values can be used for each of the methods presented above.  
Reliability Estimation Incorporation 
The determined metric values represent the level of confidence in thermal or 
material information that is available for a part. This confidence can be converted to an 
uncertainty level for specific parameters in reliability models. A part with a higher MIA 
61 
 
 
or TIA value (more information available) implies that the parameters related to this 
information will have a lower level of uncertainty. Alternatively, parts that do not have 
a high level of information availability will have higher uncertainty levels in parameters 
and thus a wider failure distribution.  
One implementation of this is through the conversion of the temperature level 
from an ambient to junction location. The model temperature requires being evaluated 
at the point of failure, which for all die level mechanisms is the junction temperature. 
The application conditions will generally be provided in terms of an ambient 
temperature of the entire system. Equation 16 can be modified to include uncertainty 
terms as follows: 
𝑇𝑗 = 𝑋(𝑇 ̅̅ ̅𝑎𝑚𝑏) + [𝑁(𝑅𝑡, 𝛽) ∗ 𝑋(𝑃𝑑𝑖𝑠𝑠)] 18 
where 𝑋(𝑇𝑎𝑚𝑏) is a generalized ambient temperature distribution, 𝑋(𝑃𝑑𝑖𝑠𝑠) is a power 
dissipation distribution, 𝑅̅̅ ̅𝑡 is the mean thermal resistance value determined through the 
datasheet, comparison with similar parts, or other method, and 𝛽 is the uncertainty in 
the thermal resistance. 
The ambient temperature and power dissipation distributions are determined 
based on collecting information from the application environment. Determining the 
thermal resistance uncertainty is much more difficult and is not provided by the 
manufacturer. The TIA value can be implemented to provide an estimate on the 
uncertainty in the thermal resistance. Using the method provided in equation 19, the 
uncertainty in the thermal resistance will be minimized when TIA is maximized. 
62 
 
 
̅̅𝑅̅𝑡
𝛽 = [1 − 𝑇𝐼𝐴] + 𝛼 19 
𝑞
where 𝑅̅̅ ̅𝑡 is the best estimate on the thermal resistance (typically value provided in the 
datasheet or parts with the same package type), 𝛼 is the minimum uncertainty level ‘po 
and 𝑞 is a severity factor that controls the magnitude of the uncertainty and is defaulted 
to 100 (or the noise will be related to 1% of the expected value). 
Comparison of Parts 
The benefit of using the metrics for comparison of parts is that it provides a 
standardized method of evaluating the information provided for a part irrespective of 
the manufacturer or method in which the information is presented. Without the metrics, 
it can be difficult to compare parts without knowing what information is expected 
regarding thermal or material parameters. The metrics also combine multiple aspects 
into a single, comparable factor. In addition to the final metric, individual aspects of 
each of the metrics can be compared to get a more specific analysis, such as comparing 
the ratings multipliers of different parts. Some comparisons of parts are provided in the 
case study presented later in this thesis.  
Any method can be used to compare the metric values between parts such as 
cosine similarity or Euclidian distance. These methods combine both of the metrics and 
result with a single value relating two parts. Cosine similarity is used when the 
magnitude of the values is not important, whereas Euclidian distance incorporates the 
actual values. When using the metric values, the Euclidian distance method makes 
more intuitive sense.  
63 
 
 
𝐷𝑖𝑠𝑡(𝑥 → 𝑦)𝐸𝑈𝐶 = √(𝑥
2
𝑇𝐼𝐴 − 𝑦𝑇𝐼𝐴) + (𝑥
2
𝑀𝐼𝐴 − 𝑦𝑀𝐼𝐴)  20 
(𝑥𝑇𝐼𝐴𝑦𝑇𝐼𝐴 + 𝑥𝑀𝐼𝐴𝑦𝑀𝐼𝐴)
𝐷𝑖𝑠𝑡(𝑥 → 𝑦)𝐶𝑂𝑆 =  21 (𝑥 2 2𝑇𝐼𝐴 + 𝑥𝑀𝐼𝐴) + (𝑦𝑇𝐼𝐴 + 𝑦𝑀𝐼𝐴)
Generalization and Comparison of Manufacturers or Part Types 
It should not be assumed that all parts from the same manufacturer will have 
the same amount of information provided or final metric values. A prime example of 
this is commercial vs. military or space grade parts that may present information 
through different documentation [9], [10]. Part manufacturers also produce parts of 
several types and structures and may have different methods of presentation and 
content for each. Part manufacturers are also commonly involved in mergers and the 
consolidation of the market can lead to large problems with information consistency 
and availability [72]–[74]. Before a merger, each manufacturer has their own baselines 
and standards for information to be shared which may not be aligned or resolved after 
the merger. Any analysis completed on a manufacturer must be re-evaluated after any 
change in status. These reasons show the strong need for evaluating information 
availability metrics at a part level but also promote comparisons of information both 
within and outside the same company.  
The generalization of metric values can be completed over many scales if 
proper considerations are put in place. The metric could be generalized for all parts 
within a specific category such as all power IGBTs or LEDs with a specific package. 
More broadly, the metric could be evaluated over an entire company. At this level, the 
comparison could be to determine the consistency of information over the entire 
64 
 
 
company or compare with other companies. A summary of the common generalizations 
that could be completed is shown in Figure 25.  
 
Figure 25: Summary of comparison methods for generalizing metric values 
In most cases it is not feasible to find all information and evaluate the metrics 
for all parts within a manufacturer or even subcategory within the manufacturer. A 
method to solve this problem is to select a subset of parts from the category or 
manufacturer and determine the metric value for each part. Then, statistical analysis 
can be completed on the dataset of metric values such as determining the mean, 
standard deviation, minimum, and maximum values. This information can be used to 
make comparisons and judgements between parts from a manufacturer or compare 
different manufacturers. 
An alternative method that will become more feasible in the coming years is 
the web scraping of information. When detailed part information pages in the same 
format are provided for each part by a manufacturer the need for manual reading and 
interpretation can be removed and automated. A script is developed to read and store 
65 
 
 
the information that is available for each part and then the same statistical analysis can 
be completed. The current pitfalls with this method include requiring the same .html 
format for parts to work properly and that not all datasheet information or parameters 
are included in the part information pages. There is a trend towards more information 
being readily available but the .pdf datasheet is still the dominant method of sharing 
information.  
Verifying and Adjusting Multiplier Level Values 
The metric multiplier values provided in the above tables for both TIA and MIA 
were determined through discussions and analysis of datasheets and other available 
information for parts. Continued discussions were completed to change the number of 
levels and values for each multiplier. Depending on the user of the metrics, the levels 
may be adjusted for specific interests and intended uses. For example, a user interested 
in gathering information for a large group of parts may want to apply a heavier penalty 
when information is not available on the part information page. An application with 
high ambient temperatures may put higher focus on the ratings multiplier within TIA. 
Adjustment of these values can be completed through discussions amongst peers from 
varied backgrounds (such as with the development of an FMEA), through an online 
survey from interested parties, or based off of the results of reliability assessments.   
The verification of the metric multiplier values can be completed ideally 
through a large-scale analysis of parts across many different manufacturers and types 
of parts. By determining the multiplier values for each part, the percentage of the total 
66 
 
 
part set with each specific level can be used as a method of verification. The multiplier 
level values would now represent the percentage of parts that met the required 
conditions. For example, if 10% of parts provided both a thermal resistance and power 
dissipation value, the TIA conversions multiplier could be set to 0.9 as a reflection of 
the 10% with the best level of information. The percentage of parts with each 
subsequently lower multiplier level would then be used to determine the remaining 
metric levels. In a less quantitative fashion, verification of the values can be completed 
through comparing the averaged metric final values for manufacturers and evaluating 
if the hierarchy of those values matches the expectations of companies in the industry. 
Case Study Analysis 
To evaluate the available information and determine the common combinations 
of metric values, a list of parts was analyzed. All parts are COTS devices to be used in 
a more demanding application. A wide range of part types from different manufacturers 
have been provided and are shown in Table 22. 
Table 22: List of parts for case study analysis 
Part ID Part ID 
Manufacturer Part Description Manufacturer Part Description 
Number Number 
Multi-chip 
1 Abracon MEMS oscillator 12 Micron 
memory 
Active pixel 
2 Aptina 13 Rohm Zener diode 
sensor 
Current sense 8-bit 
3 14 
amplifier microcontroller 
Silicon Labs 
8-bit 
4 Zener diode 15 
Diodes Inc. microcontroller 
5 Hall effect sensor 16 ST Micro 6-axis IMU 
Pre-biased Texas 
6 17 Linear regulator 
transistor array Instruments 
67 
 
 
7 Schottky diode 18 Mobile processor 
Temperature 
8 DC/DC converter 19 
sensor 
9 DC/DC converter 20 RS485 transceiver 
Linear Tech 
Current sense 
10 21 CAN transceiver 
amplifier 
11 DC/DC converter 22 Vishay Zener diode 
 
All available information was gathered for each of the 22 parts. Using this 
information, comparisons of the manufacturer’s and part’s information availability 
across many categories such as thermal information, material information, and 
reliability modeling required information. This information is used to draw conclusions 
about the information availability for part types and manufacturers and will be 
incorporated into reliability estimations. This list of parts should not be considered as 
representative for all electronic parts. These parts have already been selected for 
consideration in a space application and thus may have more information provided than 
the typical part. The parts are organized into the following part types: 
Table 23: Part numbers with associated categories 
Converters / 
Category Transistors Sensors Amplifiers Diodes Processors 
Transceivers 
12, 14, 
Part ID 4, 7, 13, 8, 9, 11 
1, 6 2, 5, 16, 20 3, 10 
Numbers 22 17, 20, 21 
15, 18 
 
Thermal information is the first key information area that was analyzed. For 
each of the parts, the datasheet parameters for all temperature ratings and thermal 
information was gathered to incorporate into the reliability estimations and determine 
the TIA values. Table 24 shows a summary of the information collected for each of the 
68 
 
 
parts. An operating temperature range was found for all parts and power dissipation / 
thermal resistance information was provided sporadically. One interesting finding is 
that of the 10 parts that provided junction operating temperature ranges, 9 provided 
thermal resistance values. Alternatively, only 2 of the 9 parts that used ambient 
operating temperature ratings provided thermal resistance values.  
Table 24: Thermal information collected for parts 
Min Power 
Pat ID Max Op. Temp. 
Category Op. Diss. 𝑹  Provided? 
Num. Temp Location 𝒕
Temp Provided? 
1 Sensors -30 70 Ambient *  
2 Amplifiers -40 85 Ambient *  
Converters / 
3 -40 85 Ambient  * 
Transceivers 
4 Processors -25 85 Operating   
5 Sensors -40 85 Ambient   
6 Processors -40 85 Ambient * * 
7 Transistors -40 105 Ambient   
Converters / 
8 -40 125 Junction  * 
Transceivers 
Converters / 
9 -40 125 Junction  * 
Transceivers 
10 Processors -55 125 Ambient   
Converters / 
11 -40 125 Junction  * 
Transceivers 
Converters / 
12 -40 125 Ambient * * 
Transceivers 
Converters / 
13 -55 125 Ambient *  
Transceivers 
14 Processors -55 135 Ambient   
15 Diodes -65 150 Junction * * 
16 Sensors -40 150 Ambient *  
17 Transistors -55 150 Junction * * 
18 Diodes -55 150 Junction  * 
19 Amplifiers -55 150 Junction  * 
20 Diodes  150 Junction *  
21 Sensors -55 150 Junction  * 
22 Diodes -55 150 Junction  * 
 
69 
 
 
Figure 26 shows the minimum and maximum temperature operating 
temperature rating values provided for each part and are color sorted by the category 
of part per Table 23. It is important to note that the values are directly from the part 
datasheets and have not been converted to account for distinct locations of 
measurement (such as ambient vs. junction). Additionally, jitter has been applied to the 
points to avoid direct overlap of points and every part’s rating is represented by the 
intersection of lines on the plot. 
 
Figure 26: Comparison of minimum and maximum operating temperature values for 
each part 
There is no direct relationship between the type of parts and the operating 
temperature ratings that are seen. Interestingly, the sensors group of products provided 
the widest variance in rating values and the converters / transceivers group provided 
70 
 
 
the most consistent rating values. All of the diodes analyzed provided a maximum 
temperature value of 150 ℃ (all also used a junction temperature location). The most 
common temperature rating was found to be (-55 ℃, 150 ℃) and made up of 23% of 
the total population of parts. The most limiting parts were found to only have a 
maximum temperature of 70 ℃ and a minimum temperature of -25 ℃. Using this 
information, the three different multiplier factors for the TIA metric were determined 
(conversions, ratings, location). A comparison plot of the ratings and conversions 
multiplier factors is in Figure 27. Both multipliers are between 0 and 1 but only the 
regions where data points were found have been plotted. 
 
Figure 27: Part TIA rating value and TIA conversion value for the sample part list 
Figure 27 shows that none of the parts have a combination of high conversion 
and rating TIA multiplier levels. Parts that provide a high conversion value are much 
more likely to provide a lower number and quality of temperature ratings. Only 2 parts 
71 
 
 
provided enough information to receive the highest conversions level, and both of those 
provided the lowest information in terms of ratings of all the sampled parts. The same 
is seen for high ratings values which are less likely to provide conversion information. 
Not shown in the figure, 21 of the 22 parts provided a specific location for their absolute 
maximum rating and received a high value for the location multiplier aspect of TIA. 
Using these values, the final TIA metric value can be determined (see Figure 28). 
 
Figure 28: Final TIA Value for different categories of parts 
There is a wide range in final TIA values and again no specific trends based on 
types of parts. Diodes provided the highest average value TIA value at 0.42. The 
diode’s parts also had the highest maximum value and the highest minimum value. The 
72 
 
 
amplifiers provided the lowest average value of 0.147. A summary of the mean, 
minimum, and maximum values is provided in Table 25. 
The material information for each part was also collected. Using this 
information, the MIA multipliers were determined with the results shown in Figure 29. 
Five of the 22 parts did not provide tabular or IPC 1752 information. The most common 
combination of multiplier level values was 0.8 for access (the information is provided 
online but not on the part information page) and 0.9 for content (tabular information 
but not the official IPC 1752 documentation). Unlike with the multipliers in TIA, as a 
higher access value is found for a part, it is likely that a high content value will be 
found. Using this information, the final MIA values can be determined. The statistical 
analysis on the groups for MIA is shown in Table 25.  
 
Figure 29: Comparison of MIA content and access multiplier values for each part 
 
73 
 
 
Table 25: Statistical analysis of part category TIA and MIA values. Highlighted red 
and green values are lowest and highest mean values subsequently.  
 Temperature Information Material Information Availability 
Availability 
Mean Min Max Mean Min Max 
Part Category (Count) 
Value Value Value Value Value Value 
Amplifiers (2) 0.147 0.014 0.28 0.86 0.72 1.00 
Converters / 
0.292 0.080 0.50 0.518 0.05 0.72 
Transceivers (6) 
Diodes (4) 0.42 0.280 0.70 0.665 0.50 0.72 
Processors (4) 0.183 0.080 0.45 0.63 0.18 0.90 
Sensors (4) 0.269 0.014 0.50 0.39 0.06 0.72 
Transistors (2) 0.39 0.080 0.70 0.81 0.72 0.90 
 
The amplifier category of parts provided the highest average MIA value and 
one of the amplifier parts provided the highest possible value of 1. The sensors category 
provided the lowest average value of only 0.39. A plot comparing the TIA and MIA 
values for each part is shown in Figure 30. Generally, parts that have a higher TIA 
value will also have a higher MIA value. The converse of this is not true, as parts with 
high MIA values can have high or low TIA values. The diodes category of parts 
provided the most combined thermal and material information compared with the other 
groups.  
74 
 
 
 
Figure 30:  Comparison of MIA and TIA values for each part 
Based off the TIA and MIA values for each part, the similarity between the 
parts can be determined. The Euclidian distance similarity was completed between the 
parts from the same category and shown in Figure 31. The comparison value between 
any two parts from the same category is the intersection of the two parts on the x and 
y axis. With Euclidian distance, darker colors are closer to 0 and represent parts that 
are more similar. In the case where the same part is compared with itself (along the 
diagonal of the diagram in Figure 31) the distance is 0. The processors category 
provided the most similar level of information while the transceivers category provided 
different levels of information.  
75 
 
 
 
Figure 31: Euclidian distance similarity between parts based on TIA and MIA value 
(higher numbers are less similar) 
Statistical analysis was also completed based on manufacturers. This can be 
used for determining the consistency of information from a single manufacturer across 
multiple types of parts. The results from the analysis are shown in Table 26. For thermal 
information, Texas Instruments provided the highest mean value of 0.49 (over 5 parts). 
Abracon and Micron both provided the highest material information value of 0.90. One 
processor provided by ST Micro provided the lowest TIA and MIA values. This does 
not mean that ST Micro in general provides low information, just that the one sample 
in this case study did not provide elevated levels of information. As discussed in the 
metrics section, the generalization of these values for a manufacturer requires a large 
76 
 
 
enough sample size to accurately capture the scope of products provided by the 
manufacturer.  
Table 26: Statistical analysis of MIA and TIA values for different manufacturers 
 Temperature Information Material Information 
Availability Availability 
Mean Min  Max  Mean  Min  Max  
Manufacturer (Count) 
Value Value Value Value Value Value 
Abracon (1) 0.080 0.080 0.080 0.900 0.90 0.90 
Aptina (1) 0.280 0.280 0.280 0.060 0.06 0.06 
Diodes Inc (5) 0.462 0.280 0.700 0.752 0.60 1.00 
Linear Tech (4) 0.066 0.014 0.090 0.585 0.18 0.72 
Micron (1) 0.080 0.080 0.080 0.900 0.90 0.90 
Rohm (1) 0.280 0.280 0.280 0.720 0.72 0.72 
ST Micro (1)  0.014 0.014 0.014 0.180 0.18 0.18 
Silicon Labs (2) 0.100 0.100 0.100 0.720 0.72 0.72 
Texas Instruments (5) 0.490 0.450 0.500 0.478 0.05 0.72 
Vishay (1) 0.350 0.350 0.350 0.500 0.50 0.50 
 
As an example, the comparison of the information for each part from Texas 
Instruments is shown in Figure 32. From the case study list there were 3 transceivers, 
1 processor, and 1 sensor from Texas Instruments. The three transceivers did not have 
similar levels of information provided. The information available from the sensor was 
comparable with the processor and one of the transceivers. For comparing a 
manufacturer, the ideal case would be the same level of (high) information for all parts 
and thus low Euclidian distance.  
77 
 
 
 
Figure 32: Euclidian distance similarity between Texas Instruments parts (higher 
numbers are less similar) 
 
  
78 
 
 
Chapter 5: Software Implementation and Analysis 
Combining the part information databases, application condition collection and 
approximation methods, and information availability metrics, a time to failure 
distribution is determined. Figure 33 shows the overall implementation encompassing 
the sources of information that impact the final time to failure distribution (blue circles) 
and hyper parameters that must be selected based on the type of analysis and 
engineering judgement (red text), like the kernel bandwidth levels for each application 
condition input and the q value that controls the severity of the thermal information 
availability (TIA) on the time to failure distribution.  
 
Figure 33: Software Implementation flowchart with information sources (blue 
circles) and hyper parameter (red text). 
79 
 
 
A Monte-Carlo Sampling method is used to determine the final time to failure 
distribution. Distributions are approximated for each input and many samples (n) are 
drawn from each to determine a time to failure distribution. The final distribution (Τ(𝑡)) 
can then be analyzed based on application requirements and reliability goals. For 
example, the time to a certain X percentage of failures is simply the distribution value 
at which X percent of the samples have failed. This is also equivalent to the probability 
that a part will fail (i.e. a part has a 1% chance to fail is equivalent to the probability 
that 1 part will fail if 100 are in a population). Additionally, the probability that a part 
will fail by a certain period is equivalent to the percentage of samples at the specified 
time in the time to failure distribution. Figure 34 shows a sample distribution generated 
with a noisy normal distribution and is analyzed with commonly used practices. The 
green dashed line is the mean time to failure (50% of the samples have failed), the 
orang dashed line shows that there is a 16% probability that a part will fail at or before 
8 years, and the red dashed line shows that a part will have a 90% chance of failure will 
occur at 12.5 years.  
80 
 
 
 
Figure 34: Sample time to failure distribution (simulated data) showing analysis of 
time to certain percentage of failures (red line) and the probability of failure for a 
certain length of time (orange dashed line). 
This methodology can be used in a number of ways to compare parts across 
different application environments and reliability expectations. Primarily, the 
methodology gives a time to failure distribution based on specific part parameters and 
application conditions. It can also be used to evaluate the impact that changes in part 
parameters or application conditions will have on the failure distribution. This means 
that completing comparisons of differently rated or designed parts (such as a 
commercial part compared to a military grade part), or different environments can be 
completed to determine potential impact. Using the thermal information availability 
metric, the methodology can also evaluate the impact on the failure distribution that 
81 
 
 
different levels of information uncertainty has. Examples with each of these cases are 
presented in the sections below.  
Single Part Reliability Estimation  
Part reliability was approximated with the following part and model constant 
parameters (see Table 27) for the TDDB failure mechanism model. In this case, the 
part parameters and model constants were treated as point estimates (not distributions) 
to show the impact that the application conditions have on the time to failure 
distribution.  
Table 27: Sample Part Part Parameters and Model Constants 
Parameter Unit Value 
Oxide Thickness nm 2 
Maximum Power 
mW 0.7 
Dissipation 
Thermal Resistance °C/W 5 
Node Size nm 35 
A0 Model Constant N/A 2.25E+03* 
Gamma Model Constant N/A 2.33* 
Activation Energy eV 0.4 
 
Application information was simulated for gate voltage, temperature, drain 
source voltage, and drain source current values using noisy normal distributions. The 
resulting time series data, which serve as the inputs for the analysis, are shown in Figure 
35. Using this data, the output samples are generated using the time series data 
distribution approximation method detailed in Chapter 3. An example comparison 
82 
 
 
input and output distribution of temperature values is shown in Figure 36 where 5000 
output samples are sampled.  
 
Figure 35: Simulated application condition information for TDDB mechanism model 
parameters.  
 
83 
 
 
 
Figure 36: Comparison of input and output samples using kernel density distribution 
approximation method. The top plot shows the input samples and the kernel density 
that was approximated (black line). The bottom plot shows the final samples 
generated using the kernel density distribution.  
Using this simulated information and selected part parameters modeling 
constants, the time to failure can be calculated for each sample and thus a distribution 
of time to failure is determined. In this case, the modeling constants and part parameters 
are held constant to evaluate the impact that the application condition distributions have 
on the failure distribution. This distribution is shown in Figure 37.  
84 
 
 
 
Figure 37: Time to failure distribution for a single part generated from 5000 samples 
from application condition distributions. Dashed lines show the time at which 1%, 
5%, and 50% of all samples will fail.  
Comparison of Failure Distribution with Different Part Parameter 
One common comparison is between similar parts with a different feature or 
parameter. For example, when transferring to a new generation of part with a smaller 
node size, geometric features about the part will change which can impact reliability. 
This is exemplified by the example below where the oxide thickness layer parameter is 
changed between 1 and 2 nm. All other factors (application conditions, model 
constants, other part parameters) are unchanged from the first example. Using this 
information and 5000 samples, both TDDB time to failure distributions are shown in 
Figure 38 and the time to X% failures are shown in Table 28. The results show that by 
85 
 
 
halving the oxide thickness, the time to failure is drastically reduced, with the mean 
time to failure reduced 5-fold.  
          
Figure 38: Projected TDDB time to failure for different oxide thicknesses (all other 
inputs remained constant). Gate voltage of 1.08 determined by using relationships 
between oxide thickness, node size, and gate voltage (see Chapter 3).  
 
Table 28: Time to X% Failure for Different Oxide Thickness (all other inputs held 
constant) 
  Time to Failure (Years) 
Percent 𝑡𝑜𝑥= 2.0 nm 𝑡𝑜𝑥= 1.0 nm 𝑡𝑜𝑥= 1.0 nm 
Failure 𝑉𝑔 =1.35 V 𝑉𝑔= 1.08 V* 𝑉𝑔= 1.35 V 
1 % 5.25 1.15 0.41 
5 % 7.87 1.88 0.73 
10 % 9.94 2.82 1.15 
25 % 14.64 4.93 2.41 
50 % 23.35 9.02 4.74 
86 
 
 
Comparison of Different Temperature Distribution Approximation Methods 
To compare the accuracy of application condition approximation methods, the 
temperature of a computer CPU (i7-8550U) was monitored for 24 minutes during 
normal usage (browsing the web, watching videos, programming). Data was collected 
using the RealTemp program and temperature was collected each second. This 
represents the time series collection approximation method. By comparison, the 
maximum junction temperature for the processor is 100 ℃ [75]. Figure 39 shows a 
comparison of the results from the data collection and references the maximum junction 
temperature.  
 
Figure 39: Comparison of collected temperature information and processor 
maximum junction temperature.  
Using this information, the kernel distribution for the sensor collected data was 
determined and is plotted in Figure 40. An assumed normal distribution was also 
87 
 
 
created to represent the application based on the maximum junction temperature. The 
distribution is made up of the same number of samples (1440 points) with a mean value 
of 85 ℃ and standard deviation of 5 ℃ (see red line in Figure 40). Using these 
distributions, 5000 output samples are drawn and used to form the time to failure 
distributions which are plotted in Figure 41. The junction failure distribution uses a 
constant value of 100 for each sample. The results show that without using a 
distribution to approximate the application, the time to failure distribution is drastically 
reduced. Even when an assumed junction distribution which remains below the 
maximum value is selected, the time to failure distribution projects failure in half the 
amount of time of the measured value distribution. This is seen more clearly in  
Table 29 which shows the time to X% failure for each of the failure 
distributions.  
 
Figure 40: Comparison of measured values kernel approximation distribution, 
assumed normal distribution below the maximum junction temperature, and the 
maximum junction temperature.  
88 
 
 
 
Figure 41: Comparison of TDDB time to failure distribution for different temperature 
distribution approximation methods. The Junction distribution was determined by 
using a constant value of 100 ℃ for all samples.  
 
Table 29: Comparison of Time to X% Failure for Different Temperature Distribution 
Approximation Methods 
 Time to Failure (Years) 
Junction  
Percent Failure 
Measured Values Junction Distribution (Constant Value) 
1 % 1.82 0.91 0.59 
5 % 2.34 1.22 0.74 
10 % 2.98 1.54 0.96 
25 % 4.22 2.2 1.37 
50 % 5.85 3.11 1.84 
75 % 7.85 4.31 2.42 
90 % 12.85 6.78 3.98 
95 % 15.97 8.65 5.03 
99 % 21.68 12.22 6.62 
 
 
89 
 
 
Comparison of Temperature Information Availability Values on Failure Distributions 
Using the thermal information metric developed in Chapter 4, a comparison can 
be completed. In this case, the same parameters as with the first example in Chapter 5 
are used but with different TIA values. The two values selected are 0.1 and 1, 
representing the cases where minimal and maximum thermal information are provided. 
Higher TIA values lead to lower uncertainty in the thermal resistance parameter. A q 
value of 10 was selected, meaning that the impact of the TIA value on the thermal 
resistance standard deviation is divided by 10. The results of this analysis are shown in 
Figure 42. The distributions themselves are similar, but the low TIA value corresponds 
with a wider overall distribution. The time to X% failures are shown in Table 30.  
 
Figure 42: TIA Comparison Failure Distributions 
90 
 
 
Table 30:  TIA Comparison Percentage Failure Time to Failure Distribution 
TIA = 0.1 TIA = 1.0 
Percent Failure 
Mean STD Mean STD 
1 % 9.72 0.88 8.89 0.24 
5 % 11.00 0.60 10.62 0.14 
10 % 12.23 0.23 11.89 0.12 
25 % 16.04 0.90 15.58 0.15 
50 % 22.66 2.75 22.35 0.16 
 
Evaluation of Different Sample Sizes 
Another important attribute that is selected is the number of samples that are 
drawn frm each input distribution and make up the final time to failure distribution. 
Intuitively, the more samples drawn from each distribution, the more accurately the 
underlying distributions are represented and thus a more accurate estimation on the 
time to failure. The impact of different output samples was evaluated for 5 different 
levels using the same part parameters and application condition information. The 
resulting distributions are shown in Figure 43. In this case, a kernel density method was 
used to generate a distribution instead of a histogram result in order to better visualize 
the data. Table 31 shows the time to X% failure for each sample size value.  
91 
 
 
 
Figure 43:Comparison of different sample sizes on failure distribution 
 
Table 31: Time to X% Failure for Different Output Sample Sizes 
 Time to Failure (Years) Based on Distribution Sample Size 
Percent Failure 100 500 1000 5000 10000 
1 % 6.25 5.85 5.4 4.86 4.91 
5 % 8.87 7.42 7.89 7.65 7.64 
10 % 9.94 9.48 10.03 9.96 9.93 
25 % 14.85 13.96 14.97 14.6 14.66 
50 % 23.31 23.39 23.98 23.4 23.99 
 
  
92 
 
 
Chapter 6:  Contributions and Future Work 
This thesis has developed an information-based reliability assessment to 
incorporate sources of uncertainty in part parameters, application conditions, and 
model constants into projections for die-level semiconductor wearout mechanisms. 
This included determining the sources of information which are available for 
commercial off the shelf (COTS) devices and can be used for reliability projections. 
This is also compared with the information that is provided for non-COTS devices 
(military, space, automotive grade parts).  
The availability of thermal and material information of individual parts is 
quantified using metrics and can be incorporated into the time to failure projections. 
Methods have been developed to generalize metric values and draw comparisons 
between parts. Trends in information availability were analyzed and determined using 
a case study of COTS parts.  
Additionally, numerous methods have been developed to approximate 
application condition and part parameter distributions. This includes a method of 
converting sensor collected application information into a distribution which can be 
sampled from and a process of using node or feature size information to select 
geometric part parameters. These methods are fully integrated into the reliability 
estimation methodology. Using this system, comparisons between different 
components, applications, and levels of information availability can be analyzed. 
93 
 
 
Future implementations can expand the list of failure mechanisms beyond what 
is discussed in this thesis. The same principles of modeling application conditions and 
part parameters apply to all failure models. Additionally, large scale data gathering 
methods can be used to mass collect information about parameters. This will lead to 
better defined correlations between part parameters and standardized metric values 
based on the type of component and manufacturer. These metrics can be further 
integrated into the reliability methodology and parameter values can be optimized using 
known time to failure data. There are also many unique situations and considerations 
that have not been considered in this thesis. This includes cases where a COTS 
component is purchased by a third party, tested and qualified to a higher-level part 
rating, and then refinished to represent this change. This additional information must 
be provided and analyzed accordingly.  
Evaluating an comparing the validity of information provided for different 
rating parts is another area where improvements can be made. Understanding if the 
provided information is accurate has predominately been assumed in this thesis but is 
not necessarily true. Through physical testing of different parts in comparison with part 
specifications, the validity of the information can be completed.  
94 
 
 
Appendices 
Appendix A: Time to Failure Distribution Python Code  
import numpy as np 
import pandas as pd 
import matplotlib.pyplot as plt 
import seaborn as sns 
from sklearn.neighbors import KernelDensity 
import openpyxl 
import matplotlib 
 
def inputExtracter(samples,samplesName,numOutputs,kernelBandwidth = 0.5,extraSpace = 2,figureSize = 
(14,8),plot=True): 
    """ 
    This function determines an approximate kernel function around an input data space and determines a certain 
number 
    of output points based on the fit distribution. 
    *Variables*: 
    samples: Inputs 
    samplesName: Identifyer for the samples (will show on produced plots) 
    numOutputs: Number of final data points to make 
    """ 
    sampleRange = np.linspace(min(samples) - extraSpace,max(samples) + extraSpace, 200) 
    kde = KernelDensity(bandwidth=kernelBandwidth,kernel='gaussian').fit(samples) 
    prediction = np.exp(kde.score_samples(sampleRange.reshape(-1,1))) 
    comps = pd.DataFrame() 
    comps['sampleRange'] = sampleRange 
    comps['Prob'] = prediction 
    comps['ProbCuma'] = np.cumsum(comps.Prob) / sum(comps.Prob) 
    testPoints = np.random.rand(numOutputs) 
    vals = [comps.sampleRange[comps[comps.ProbCuma > i].index[0]] for i in testPoints] 
    if plot == True: 
        plt.figure(figsize=figureSize) 
        plt.subplot(2,1,1) 
        plt.title(samplesName) 
        labelString = "Input (" + str(len(samples)) + ") Samples" 
        numBins = round(len(samples) / 1) 
        plt.hist(samples,numBins,faceColor='b',alpha=.5,label=labelString) 
        plt.plot(sampleRange[:,None],max(np.histogram(samples,numBins)[0]) / max(comps.Prob)*prediction, 
                 "k-",lw=3,label = "Density Function") 
        plt.ylabel("Input Samples") 
        plt.legend() 
        plt.subplot(2,1,2) 
        labelString = "Output (" + str(numOutputs) + ") Samples" 
        numBins = round(numOutputs / 10) 
        plt.hist(vals,numBins,faceColor='c',alpha=.5,label = labelString) 
        plt.plot(sampleRange[:,None],max(np.histogram(vals,numBins)[0]) / max(comps.Prob)*prediction, 
                 "k-",lw=3,label="Density Function") 
        plt.ylabel("Output Samples") 
        plt.legend() 
        plt.xlabel(samplesName) 
    return vals, kde 
 
95 
 
 
def TDDB(gamma,T,Vt,tox,Ea,A=1,k=8.617e-5): 
    """Determines the estimated time to failure for the time dependent dielectric breakdown E model method. 
    The application conditions of T and Vt should be supplied as arrays of information whereas the other inputs 
    should be single inputs.""" 
    estimate = A*np.exp(-gamma*np.array(Vt) / tox)*np.exp(Ea / (k*np.array(T))) 
    return estimate 
 
def stringChecker(target,string): 
    """Determines if a target is located within a strnig. Function is used to grab the information using only general 
terms.""" 
    correct = [s for s in string if target in s] 
    if len(correct) == 1: 
        return correct[0] 
        return value 
    if len(correct) > 1: 
        print("Please refine target (Mulitple Options: ") 
        print(correct) 
    if len(correct) == 0: 
        print("No string found") 
 
def conditionPlotter(infoFrame,titleString = 'Input Feature Information',figWidth=14,figHeight=5): 
     
    time = infoFrame.columns.tolist()[0] 
    features = infoFrame.columns.tolist()[1:] 
    plt.figure(figsize=(figWidth,figHeight*len(features))) 
    font = {'family' : 'serif', 
            'weight' : 'normal', 
            'size'   : 12} 
    matplotlib.rc('font', **font) 
    for i,feature in enumerate(features): 
        plt.subplot(len(features)+1,1,i+1) 
        if i == 0: 
            plt.title(titleString) 
        plt.plot(infoFrame[time], 
                 infoFrame[feature],'bo',markersize=5) 
        plt.ylabel(feature) 
        plt.grid(axis='x') 
        plt.xlim(0,len(infoFrame[features[0]])+1) 
    plt.xlabel(time) 
 
def failurePlotter(failureDistribution,pcts,figSize = (14,8),stringTitle='Time to Failure Distribution'): 
    sortedFails = np.sort(failureDistribution) 
    failTable = [round(sortedFails[int(round(i / 100*len(failureDistribution)))],2) for i in pcts] 
    ft = pd.DataFrame() 
    ft['Percent'] = pcts 
    ft['TTF'] = failTable 
 
    plt.figure(figsize=figSize) 
    numBins = int(numOutputs / 15) 
    plt.ylim(0,max(np.histogram(timeFail,numBins)[0])+5) 
    plt.title(stringTitle) 
    plt.hist(failureDistribution,bins=numBins,histtype='step') 
    for row in range(len(pcts)): 
        pctString = 'Time to ' + str(ft.Percent[row]) + "% Failure: " + str(round(ft.TTF[row],2)) + ' Years' 
        plt.plot([ft.TTF[row],ft.TTF[row]],[0,max(np.histogram(timeFail,numBins)[0])+5],'--',lw=3,label=pctString,) 
 
    plt.ylabel('Frequency') 
    plt.xlabel('Time (Years)') 
96 
 
 
    plt.legend() 
    return ft 
 
def uncertaintyAdder(conditionInformation,targetStrings,stdLevel): 
    for i,value in enumerate(targetStrings): 
        original = conditionInformation[stringChecker(value,conditionInformation.columns.tolist())] 
        updated = original + np.random.normal(0,stdLevel[i],len(original)) 
        conditionInformation[stringChecker(value,conditionInformation.columns.tolist())] = updated 
 
def ThermalResistanceTIA(TIA,mean,samples,q=100,enable=True): 
    if enable == True: 
        beta = mean / q * (1-TIA) 
        newThermals = np.random.normal(mean,beta,samples) 
        return newThermals 
 
 
 
failureMechanisms = ['TDDB','HCI','EMI','NTBI','Corrosion'] 
mechanismAspects = [5,5,6,4,5] 
mechanismPartParams = [6,5,6,8,7] 
mechanismParams = {} 
for i,mech in enumerate(failureMechanisms): 
    mechanismParams[mech] = [mechanismAspects[i],mechanismPartParams[i]] 
mechanismParams 
 
 
 
selectedMech = 'TDDB' 
numPartParams = mechanismParams[selectedMech][1] 
startPointPart = 6 
endPointPart = startPointPart + numPartParams 
 
numberAspects = mechanismParams[selectedMech][0] 
numOutputs = 5000 
 
targetStrings = ['Source Voltage','Source Current'] 
uncertaintySTDLevels = [.1,.1] 
 
bandWidthLevels = [.1,.75,.001,.1] 
 
percentLevels = [1,5,50] 
 
TIA = 1 
qVal = .1 
 
numConditionSamples = 32 
 
# Importing Information 
bk = openpyxl.load_workbook("TDDB Template.xlsx") 
sheetNames = bk.sheetnames 
sheet1 = bk[sheetNames[0]] 
 
partUnits = [] 
partParamNames = [] 
partValues = [] 
# Grab parameter information (left side of excel sheet) 
partParams = sheet1['A' + str(startPointPart):'C' + str(endPointPart)] 
for parameterRow in partParams: 
97 
 
 
    partParamNames.append(parameterRow[0].value) 
    partUnits.append(parameterRow[1].value) 
    partValues.append(parameterRow[2].value) 
 
partInfo = pd.DataFrame() 
partInfo["Parameter"] = partParamNames 
partInfo["Unit"] = partUnits 
partInfo["Value"] = partValues 
# Create dictionary of information for future reference / use 
info = {} 
for row in range(len(partInfo)): 
    info[partInfo.Parameter[row]] = partInfo.Value[row] 
 
# Grab information of the condifion information (Need to supply starting and ending columns for feature info) 
conditionNames = [] 
conditionUnits = [] 
conditionValues = [] 
for col in sheet1.iter_cols(min_col = 5,max_col=4+numberAspects,min_row=5): 
    conditionNames.append(col[0].value) 
    conditionUnits.append(col[1].value) 
    colVals = [] 
    for cell in range(2,numConditionSamples-1): 
        colVals.append(col[cell].value) 
    conditionValues.append(colVals) 
 
condStrings = [] 
for name in range(len(conditionNames)): 
    condStrings.append(conditionNames[name] + " (" + conditionUnits[name] + ")") 
 
# Create information dataframe for future reference / table 
 
conditionInfo = pd.DataFrame(np.matrix(conditionValues).T,columns=condStrings) 
 
# Inject uncertainty in some features if they have uniform values / only 1 value provided. 
 
uncertaintyAdder(conditionInfo,targetStrings,stdLevel = uncertaintySTDLevels) 
 
# Split time feature off of other condition information for plotting / analysis 
 
time = conditionInfo.columns.tolist()[0] 
features = conditionInfo.columns.tolist()[1:] 
 
 
# Number of samples to use for the analysis 
information = [] 
outputSamples = [] 
models = [] 
 
# Plot the input conditions (after uncertainty is added) 
conditionPlotter(conditionInfo,figHeight=4) 
 
plt.savefig('Input Features.png') 
 
# Transform the input feature information into distribution and sample from those to form the new samples 
for i,feature in enumerate(features): 
    information.append(inputExtracter(np.array(conditionInfo[feature]).reshape(-1,1),feature, 
                                      numOutputs=numOutputs,kernelBandwidth = bandWidthLevels[i],plot=True)) 
    outputSamples.append(information[i][0]) 
98 
 
 
    models.append(information[i][1]) 
 
    plt.savefig(feature + ' Distribution Plot.png') 
 
 
# Form Dataframe of the new samples 
newSamples = pd.DataFrame(np.matrix(outputSamples).T,columns = features) 
 
# Power Dissipation calculation based on voltage and current levels 
newSamples['Power (W)'] = newSamples[stringChecker("Source Current",string=newSamples.columns.tolist())] * 
newSamples[stringChecker( 
    "Source Voltage",string=newSamples.columns.tolist())] 
 
# Convert temp from ambient to junction with power dissipation and thermal resistance 
tempA = newSamples[stringChecker("Temp",string=newSamples.columns.tolist())] + 273.15 
powerDiss = newSamples['Power (W)'] 
thermR = 
ThermalResistanceTIA(TIA,info[stringChecker('Thermal',partInfo.Parameter.tolist())],samples=numOutputs,q=q
Val,enable=True) 
tempJ = tempA + powerDiss * thermR / 1000 
 
# Grab the constants and part parameters from the dictionary and use those to make an estimate on TTF using the 
model. 
tox = info[stringChecker("Oxide",partInfo.Parameter.tolist())] 
A = info[stringChecker("A0",partInfo.Parameter.tolist())] 
Ea = info[stringChecker("Activation",partInfo.Parameter.tolist())] 
gamma = info[stringChecker("Gamma",partInfo.Parameter.tolist())] 
Vt = newSamples[stringChecker("Gate Voltage",string = conditionInfo.columns.tolist())] 
timeFail = TDDB(gamma,tempJ,np.array(Vt),tox,Ea,A=A) / (365*24*60*60) 
 
# Determine percents of interest and plot the final distribution 
failurePlotter(timeFail,pcts = percentLevels) 
 
plt.savefig('Time To Failure Result.png') 
 
 
 
 
 
99 
 
 
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