Reliability & Life Testing Handbook, Volume 2

Problems and reference sections are included in each chapter.

Preface

Chapter 1–Reliability and Confidence Limits for One-Shot Items or Binomial (Bernoulli) Trials

• The Binomial Distribution
• The Cumulative Binomial Distribution
• Binomial Confidence Limits
• Exact Binomial Confidence Limits

Chapter 2–Comparing Two Lots through Binomial Testing

• When And How To Apply

Chapter 3–Suspended-Items Test, And Analysis of Field and Warranty Data

• Objectives And Applicability
• Methodology And Applications
• Test Stopped When Only Part Of The Sample Has Failed-Censored Tests
• Appendix 3a-Computer Program Of The MLE Of Mixed-Weibull Distributions, Through The Em Algorithm, For Suspended Data

Chapter 4–Sudden-Death Testing

• Objectives And Applicability
• Methodology And Applications
• Step-By-Step Procedure For Sudden-Death Testing And Data Analysis
• Relationship Between The Sudden-Death Line And The Population Line
• Confidence Bounds About The Sudden-Death Test Population Line
• Sudden-Death Test Duration
• Appendix 4a-Derivation Of Equations (4.5) And (4.7)

Chapter 5–Nonparametric Testing

• Objectives
• The Success-Run Test
• The CL-Rank Test
• The Percent-Surviving Test
• The Sign Test
• The Run And Randomness Tests
• Comparison Of Two Population Means Using Their Ranges
• The Binomial-Pearson Reliability Test
• Binomial-Pearson Overload-Stress Test
• The Wilcoxon-White Rank-Sum Test For Two Independent Samples
• Appendix 5a-Derivation Of Eq. (5.1)

Chapter 6–Accept-Reject Testing With Fixed Test Time or Fixed Test Failures While Meeting Both the Consumer’s and the Producer’s Risk Requirements for the Exponential Case

• Introduction
• Figures 6.1 And 6.2 Approach
• Figure 6.3 Approach
• Justification For Using Figure 6.3 To Obtain Confidence Limits On The Mean Life
• Uses Of Figures 6.1 And 6.2
• To Find mL1
• To Find The Allowable Number Of Failures, a, Given mL1
• To Find mU1
• To Find P (R) Given mU1
• Uses Of Figure 6.3
• The Optimum Number Of Test Units For Accept-Reject Testing With Zero Failures While Meeting The Consumer’s Risk Requirement For The Exponential Case
• The Optimum Number Of Test Units For Accept-Reject Testing With One Or More Failures While Meeting The Consumer’s Risk Requirement For The Exponential Case
• Appendix 6a-The Relationships Among The Poisson (POI), Gamma (GAM), And Chi-Square (X2) Distributions

Chapter 7–Sequential Probability Ratio Tests (SPRT) For the Exponential Case

• Introduction
• SPRT
• SPRT For The Exponential Case [3]
• The Distribution Of The Successive Sums Of The Times To Failure From An Exponential Sequential Test Process
• Calculation Of The Confidence Limits
• The Operating Characteristic Curve For The Sequential Test Plan
• Expected Test Time In The Sequential Test
• MIL-Hdbk-781
• The Optimum Test Sample Size

Chapter 8–Sequential Testing On the Scale Parameter of the Weibull Distribution

• Accept And Reject Criteria

Chapter 9–Accept-Reject Tests For the Binomial Case

• When And How To Apply
• Charted And Tabulated Two-Risk Test Plans For Accept-Reject Binomial Tests

Chapter 10–Sequential Testing For the Binomial Case

• Introduction
• Test Requirements
• Binomial Sequential Test Plan Tables
• Method For Truncating The Sequential Testing Plans For The Binomial Case

Chapter 11–Bayesian MTBF and Reliability Demonstration Tests

• Bayesian Concepts
• General Procedure For Finding The Posterior Distribution
• The Exponential Prior Distribution With Exponential And Poisson Conditionals
• The Beta And Gamma Prior Distributions
• Assessment Of Prior Distributions
• Two-Risk Requirements Criteria
• Test Plans, Procedures And Comparisons
• Bayesian Reliability/MTBF Demonstration-Key Concepts Summary
• Single Prior Belief Bayesian Reliability Demonstration
• Nonidentifiable Posterior Distributions
• Appendix 11a-Determination Of The Bayesian Reliability Credible Intervals
• Appendix 11b-Determination Of The Bayesian MTBF Credible Intervals
• Appendix 11c-Determination Of The Requirements Criteria 1 Of Bayesian Testing For The MTBF
• Appendix 11d-Determination Of The Requirements Criteria 1 Of Bayesian Testing For The Reliability

Chapter 12–Accelerated Reliability and Life Tests

• What It Is, And How It Is Applied
• The Arrhenius Model
• The Eyring Model
• The Inverse Power Law Model
• The Combination Model
• The Generalized Eyring Model
• The Bazovsky Model
• Temperature-Humidity Models
• The Weibull Stress-Life Model

Chapter 13–Test Sample Size Determination

• Introduction
• Normal Distribution
• Exponential Distribution
• Weibull Distribution
• Binomial Distribution

Appendix A: Rank Tables
Appendix B: Standardized Normal Distribution’s Area Tables
Appendix C: Percentage Points, F-Distribution
Appendix D: Critical Values for Various Kolmogorov-Smirnov (K-S) Goodness-Of-Fit Tests
Appendix E: Binomial or Attribute Reliability Test Curves For Confidence Levels, CL, Of 50%, 80%, 90%, 95%, And 99%

Index