Accelerated Testing - A Practitioner's Guide to Accelerated and Reliability Testing

254 Pages·2006·3.697 MB·English

by  Dodson, Bryan, Schwab, Harry

A T
CCELERATED ESTING
A Practitioner’s Guide to
Accelerated and Reliability Testing
Bryan Dodson
Harry Schwab
Warrendale, Pa.
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Library of Congress Cataloging-in-Publication Data
Dodson, Bryan, 1962-
Accelerated testing : a practitioner’s guide to accelerated and reliabil-
ity testing / Bryan Dodson, Harry Schwab.
p. cm.
Includes bibliographical references and index.
ISB-10 0-7680-0690-2
ISBN-13 978-0-7680-0690-2
1. Reliability (Engineering). I. Schwab, Harry. II. Title.
TS173.D61 2006
620’.00452—dc22 2005057538
SAE International
400 Commonwealth Drive
Warrendale, PA 15096-0001 USA
E-mail: [e-mail]
Tel: [phone] (inside USA and Canada)
724-776-4970 (outside USA)
Fax: [phone]
Copyright © 2006 SAE International
ISBN-10 0-7680-0690-2
ISBN-13 978-0-7680-0690-2
SAE Order No. R-304
Printed in the United States of America.
P
REFACE
This book presents accelerated testing from a practical viewpoint. The material is presented
with the practitioner in mind; thus, proofs and derivations have been omitted, and numerous
examples have been included. In addition, most examples have been worked in Microsoft®
Excel and are included in the accompanying CD. For those desiring proofs and derivations,
references are provided. Our goal is that practicing engineers will be able to apply the methods
presented after studying this text.
Practitioners will fi nd this text valuable as a comprehensive reference book, but this book is
also ideal for use in college courses. In particular, it is recommended that this text be used for
one-semester college courses. Students should have a familiarity with basic probability and
statistics before attempting this material.
The text consists of eight chapters. Chapter 1 provides an introduction and overview of the
limitations of accelerated testing. Chapters 2, 3, and 4 describe the fundamentals of statistical
distributions, the most commonly used distributions in accelerated testing, and parameter estima-
tion methods. Chapter 5 describes test plans for accelerated testing, including reliability growth.
Chapter 6 explains models for accelerated aging, along with qualitative methods of accelerated
testing. Chapter 7 explains environmental stress screening (ESS), and Chapter 8 presents the
equipment and methods used in accelerated testing.
Be sure to use the accompanying CD, which contains a website to organize the material. The
CD contains the following content:
• Examples—The examples presented in the text are worked in Microsoft Excel templates.
These templates will be useful when applying the material to real-world problems.
• Statistical Tables—The statistical tables included in the appendices of books are holdovers
to times when computers were not available. These tables give solutions to closed integrals
of functions that could not be solved implicitly and required numerical methods to solve.
These functions are now included in electronic spreadsheets. When the text references a
value available in Appendix A, use the Microsoft Excel templates included on the CD.
• Burn-In Optimization—This is a Microsoft Excel template for determining the optimum
burn-in duration based on the cost of burn-in time, burn-in failures, and fi eld failures.
• Random Number Generator—This Microsoft Excel template generates random numbers
that can be used for simulations. There are random number generators for the Weibull,
normal, lognormal, and exponential distributions.
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• Government Documents—This page contains many documents in PDF format. There are
numerous military standards and handbooks related to reliability and accelerated testing.
• AMSAA Reliability Growth Handbook—This page provides the AMSAA Reliability Growth
Handbook in Microsoft Word format.
–viii–
C
ONTENTS
Chapter 1—Introduction ...........................................................................................................1
The Purpose of Accelerated Testing .............................................................................1
Design Life ...................................................................................................................2
Statistical Sample Size Determination .........................................................................5
Tolerances in Accelerated Testing ................................................................................5
Financial Considerations ..............................................................................................9
Summary ....................................................................................................................17
Chapter 2—Probability Fundamentals ...................................................................................19
Sampling ....................................................................................................................19
Probability Density Function .....................................................................................21
Cumulative Distribution Function ..............................................................................25
Reliability Function ....................................................................................................27
Hazard Function .........................................................................................................27
Expectation .................................................................................................................29
Summary ....................................................................................................................31
Chapter 3—Distributions........................................................................................................33
Continuous Modeling Distributions ...........................................................................33
Weibull Distribution ............................................................................................33
Normal Distribution ............................................................................................39
Lognormal Distribution .......................................................................................46
Exponential Distribution .....................................................................................50
Discrete Modeling Distributions ................................................................................55
Poisson Distribution ............................................................................................55
Binomial Distribution ..........................................................................................56
Hypergeometric Distribution ...............................................................................58
Geometric Distribution ........................................................................................60
Identifying the Correct Discrete Distribution ......................................................61
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Sampling Distributions ...............................................................................................61
Chi-Square Distribution ......................................................................................62
t-Distribution .......................................................................................................64
F-Distribution ......................................................................................................66
Bayes’ Theorem ..........................................................................................................68
Summary ....................................................................................................................71
Chapter 4—Parameter Estimation ..........................................................................................73
Maximum Likelihood Estimation ..............................................................................73
Probability Plotting ....................................................................................................74
Hazard Plotting ...........................................................................................................74
Exponential Distribution ............................................................................................74
Maximum Likelihood Estimation .......................................................................75
Hazard Plotting ....................................................................................................79
Probability Plotting..............................................................................................80
Normal Distribution ...................................................................................................83
Maximum Likelihood Estimation .......................................................................84
Hazard Plotting ....................................................................................................87
Probability Plotting..............................................................................................89
Lognormal Distribution ..............................................................................................91
Weibull Distribution ...................................................................................................92
Maximum Likelihood Estimation .......................................................................92
Hazard Plotting ....................................................................................................95
Probability Plotting..............................................................................................97
Nonparametric Confi dence Intervals ..........................................................................99
Summary ..................................................................................................................102
Chapter 5—Accelerated Test Plans ......................................................................................103
Mean Time to Fail ....................................................................................................103
Test Plan Problems ...................................................................................................103
Zero-Failure Testing .................................................................................................109
Bogey Testing ....................................................................................................109
Bayesian Testing ................................................................................................110
Sequential Testing ....................................................................................................119
Pass-Fail Testing ................................................................................................119
Exponential Distribution ...................................................................................125
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Weibull Distribution ..........................................................................................126
Randomization of Load Cycles ................................................................................131
Reliability Growth ....................................................................................................134
Reliability Growth Process ................................................................................135
Reliability Growth Models ................................................................................136
Summary ..................................................................................................................140
Chapter 6—Accelerated Testing Models ..............................................................................141
Linear Acceleration ..................................................................................................141
Field Correlation ......................................................................................................142
Arrhenius Model ......................................................................................................149
Eyring Model ...........................................................................................................157
Voltage Models .........................................................................................................169
Mechanical Crack Growth .......................................................................................170
Degradation Testing .................................................................................................171
Qualitative Tests .......................................................................................................176
Step-Stress Testing ............................................................................................177
Elephant Tests ....................................................................................................179
HALT and HASS ...............................................................................................179
Summary ..................................................................................................................180
Chapter 7—Environmental Stress Screening .......................................................................181
Stress Screening Theory ...........................................................................................181
The Product Reliability Equation ......................................................................181
What Is ESS? .....................................................................................................184
The Evolution of ESS ........................................................................................184
Misconceptions About ESS ...............................................................................186
Types of Environmental Stress ..........................................................................187
Advantages of Temperature Cycling .................................................................193
Levels of Screen Complexity ............................................................................195
Failure Analysis .................................................................................................196
Case Histories ....................................................................................................197
Implementing an ESS Program .........................................................................198
Equipment .........................................................................................................200
Burn-In Optimization ...............................................................................................202
Summary ..................................................................................................................205
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Chapter 8—Test Equipment Methods and Applications ......................................................207
Simulation Versus Stimulation .................................................................................208
Simulation .........................................................................................................208
Stimulation ........................................................................................................211
Types of Stresses ......................................................................................................212
Temperature .......................................................................................................212
Vibration ............................................................................................................214
Electrical Stress .................................................................................................218
Combined Environments ..........................................................................................218
Other Types of Stress ...............................................................................................218
Summary ..................................................................................................................219
Appendix A—Statistical Tables ............................................................................................221
Table A.1: The Gamma Function ..........................................................................221
Table A.2: Standard Normal Cumulative Distribution Function ...........................222
Table A.3: Chi-Square Signifi cance ......................................................................224
Table A.4: F Signifi cance ......................................................................................226
Table A.5: t Signifi cance .......................................................................................228
Table A.6: Poisson Cumulative Distribution Function ..........................................229
Appendix B—Government Documents ................................................................................231
Appendix C—Glossary .........................................................................................................233
Appendix D—List of Acronyms ...........................................................................................243
References .............................................................................................................................247
Index ......................................................................................................................................249
About the Authors ................................................................................................................255
–xii–
C 1
HAPTER
I
NTRODUCTION
The scientifi c theory of accelerated testing is highly developed, but the application of this theory
has proven diffi cult, especially in the mobility industries. The required design life for many
components exceeds 10 years, and the application environment is harsh and highly variable.
Vehicles must operate reliably in arctic conditions and in desert conditions. Driving profi les
range from the 16-year-old male to the 90-year-old female. An airliner may fl y long-haul ocean
routes for 20 years, while an identical model may fl y short-range routes that result in many
more takeoffs and landings over the life of the aircraft. Combining this variety into a realistic
test that can be completed in a reasonable time frame with a reasonable budget is diffi cult and
requires compromises.
Th e Purpose of Accelerated Testing
Ultimately, the only purpose of accelerated testing is cost reduction. The costs for accelerated
testing—components, monitoring equipment, labor, test equipment, and so forth—must be
recovered through lower warranty and the positive fi nancial impact of customer satisfaction.
Accelerated tests fall into two categories: (1) development tests, and (2) quality assurance tests.
During research, short inexpensive tests are needed to evaluate and improve performance. The
progress of a product in these development tests is often monitored statistically with a reliability
growth program. Some quality assurance tests are as follows:
• Design verifi cation
• Production validation
• Periodic requalifi cation
Quality assurance tests are often tied to statistical sampling plans with requirements such as a
demonstrated reliability of at least 95% at 10 years in service with a confi dence level of 90%.
Statistically, 95% reliability with 90% confi dence can be demonstrated by testing 45 units to the
equivalent of 10 years in service. Table 1.1 gives the required sample sizes for some common
reliability requirements.
Before proceeding with a test of 299, 45, or even 16 samples, the purpose of the test should be
investigated. What does it cost to test 299 units? The following costs should be considered:
• Prototype costs
• Instrumentation costs (results monitoring)
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TABLE 1.1
RELIABILITY DEMONSTRATION SAMPLE SIZES
Reliability Confidence Sample Size
99% 95% 299
99% 90% 229
99% 50% 69
95% 95% 59
95% 90% 45
95% 80% 31
90% 90% 22
90% 80% 16
• Setup costs
• Labor costs
• Laboratory costs (many tests take two or more months to complete)
Using the sample sizes shown in Table 1.1 allows no failures. If a failure occurs, do timing
and budget constraints allow changes and a repeat of the test? What are the implications of
bringing a product to market if that product did not demonstrate the required reliability with an
appropriate level of confi dence?
Design Life
Determining the design life to be simulated with an accelerated test can be diffi cult. Many
automobile manufacturers specify a design life of 10 years for brake systems (excluding pads),
but how does 10 years in service translate to an accelerated test? According to a study of brake
system usage for minivans in 1990, the following statements are true:
• The median number of brake applies was 322,000 for 10 years in service.
• Five percent of the vehicles had more than 592,000 brake applies in 10 years of service.
• One percent of the vehicles had more than 709,000 brake applies in 10 years of service.
• The force of the brake apply ranged from 0.1 to 1.0 g-force, with the shape of the distribu-
tion shown in Figure 1.1.
How many times should the brake system be cycled in the accelerated test representing 10 years?
Engineers design for the most stressful conditions; therefore, does this mean that the number of
cycles is determined by the most stressful driver?
User profi les are often defi ned by percentile. The 95th percentile point is the point with 5% of
the users having a more stressful profi le. One percent of the users have a driving profi le that is
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