Reliability Verification, Testing, and Analysis in Engineering Design

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ISBN: 9780824704759 | 0824704754
Cover: Hardcover
Copyright: 11/27/2002

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Striking a balance between the use of computer-aided engineering practices and classical life testing, this reference expounds on current theory and methods for designing reliability tests and analyzing resultant data through various examples using MicrosoftÂ® Excel, MINITAB, WinSMITH, and ReliaSoft software across multiple industries. The book discusses modern design reliability principles, techniques, and terms, applications of MicrosoftÂ® Excel Tool Solver and Goal Seek nonlinear search procedures for developing Fisher matrices and likelihood ratio confidence intervals, and table generation on median ranks, beta-binomial bounds, and standard percents.

Preface

iii

A Modern View of Reliability Concepts and Design for Reliability

(62)

What Is Reliability?

(12)

Definition of Reliability

(4)

What Is a Failure?

(4)

Three Reasons Why Products Fail

(2)

History of Reliability in the United States

(2)

Overview of Reliability Modeling

(9)

Six Basic Approaches to Modeling Product Reliability

(5)

Failure Mechanisms

(1)

Establishing Reliability Specifications

(3)

An Overview of Reliability Planning

(9)

Elements of Design for Reliability

(1)

Deploying Reliability Requirements

(1)

Reliability Prediction

(4)

Cost of Reliability and Product Testing

(1)

Reliability Bathtub Curve

(2)

Life-Cycle Costing

(1)

Enablers for a Successful Reliability Planning Effort

(3)

Reliability Growth Management

(1)

Exercises

(27)

Appendix 1 A. FMEA/FMECA/DVP&R

(23)

Preliminaries, Definitions, and Use of Order Statistics in Reliability Estimation

(38)

Reliability Metrics

(10)

Reliability Functions

(4)

Population Moments

(3)

Worked-Out Examples

(3)

Empirical Estimates of F(t) and Other Reliability Metrics: Use of Order Statistics

(10)

Naive Rank Estimator

(1)

Mean and Median Rank Estimators

(2)

Use of Rank Estimators of F(t) as a Plotting Position in a Probability Plot

(2)

Beta-Binomial and Kaplan--Meier Confidence Bands on Median Rank Estimator

(2)

Empirical Estimates of Other Reliability Metrics: R(t), λ(t), f(t), and H(t)

(2)

Working with Grouped Data

(1)

Working with Censored Data

(8)

Categorizing Censored Data Sets

(2)

Special Staged Censored Data Sets

(1)

Nonparametric Estimation of Reliability Metrics Based on Censored Data

(2)

Developing Empirical Reliability Estimates of Warranty or Grouped Censored Data

(2)

Exercises

(9)

Appendix 2A

(6)

A Survey of Distributions Used in Reliability Estimation

101

(34)

Introduction

101

(3)

Normal Distribution

104

(6)

Central Tendency

104

(1)

Properties of normal Distribution

105

(5)

Lognormal Distribution

110

(4)

Exponential Distribution

114

(3)

Weibull Distribution

117

(4)

Weibull Power-Law Hazard Function

117

(1)

Weibull Survival Function

118

(1)

Properties of the Weibull Distribution

118

(1)

Three-Parameter Weibull

119

(2)

Extreme Value (Gumbel) Distribution

121

(4)

Other Distributions Used in Reliability

125

(2)

Logistic and Log-Logistic Distributions

126

(1)

Gamma and Log-Gamma Distributions

126

(1)

Miscellaneous Other Noteworthy Distributions

126

(1)

Mixtures and Competing Failure Models

127

(2)

Exercises

129

(6)

Appendix 3A. Background

131

(2)

Appendix 3B. Weibull Population Moments

133

(2)

Overview of Estimation Techniques

135

(54)

Introduction

135

(2)

Rank Regression and Probability Plotting Techniques

137

(10)

Normal Probability Plotting Techniques

137

(5)

Weibull Probability Plotting Techniques

142

(5)

Maximum Likelihood Estimation

147

(12)

Introduction to ML Estimation

147

(1)

Development of Likelihood Confidence Intervals

148

(3)

Maximum Likelihood Estimation of Normal Parameters, μ and σ, for Complete Sample Sets

151

(4)

ML Estimation of Normal Parameters μ and σ2 in the Presence of Censoring

155

(2)

ML Estimation of Weibull Parameters θ and β

157

(2)

Simulation-Based Approaches for the Development of Normal and Weibull Confidence Intervals

159

(2)

Other Estimators

161

(1)

Best Linear Estimators of μ and σ

161

(1)

Recommendations for Choice of Estimation Procedures

162

(1)

Estimation of Exponential Distribution Properties

163

(10)

Estimating the Exponential Hazard-Rate Parameter, λ, or MTTF Parameter, θ

164

(2)

Exponential Confidence Intervals

166

(2)

Use of Hazard Plots

168

(5)

Three-Parameter Weibull

173

(4)

Exercises

177

(12)

Appendix 4A. Monte Carlo Estimation

181

(5)

Appendix 4B. Reference Tables and Charts

186

(3)

Distribution Fitting

189

(14)

Introduction

189

(1)

Goodness-of-Fit Procedures

189

(10)

Goodness-of-Fit Tests Based on Differences Between Empirical Rank and Fitted Distributions

190

(5)

Rank Regression Tests

195

(1)

Other Goodness-of-Fit Tests

196

(3)

Exercises

199

(4)

Appendix 5A

201

(2)

Test Sample-Size Determination

203

(50)

Validation/Verification Testing

204

(4)

Verification Testing

204

(2)

Specifying a Reliability Requirement

206

(1)

Success-Failure Testing

206

(1)

Testing to Failure

207

(1)

Strategies for Reducing Sample-Size Requirements

207

(1)

Underlying Distributional Assumption

208

(1)

Success Testing

208

(2)

Bayesian Adjustment to Success Formula

210

(1)

Success-Failure Testing

210

(7)

Use of Binomial Nomograph

211

(2)

Exact Formulas for Binomial Confidence Limits in Success-Failure Testing

213

(1)

Large-Sample Confidence Limit Approximation on Reliability

214

(2)

Bayesian Adjustment to Success-Failure Testing Formula

216

(1)

Correctness of Binomial Success-Testing Formula

216

(1)

Exponential Test-Planning Formulas

217

(8)

Success Testing Under an Exponential Distribution Assumption Using Alternate Formula

221

(1)

Extended Bogey Testing Under Exponential Life Model

222

(2)

Extended Success Testing---Exponential Distribution

224

(1)

Risks Associated with Extended Bogey Testing

224

(1)

Reduced Test Duration

225

(1)

Weibull Test Planning

225

(8)

Weibayes Formulas

226

(3)

Adequacy of Weibayes Model

229

(2)

Chrysler Success--Testing Requirements on Sunroof Products

231

(2)

Tail Testing

233

(1)

Failure Testing

234

(4)

Other Management Considerations

238

(1)

Summary

239

(1)

Exercises

240

(13)

Appendix 6A. Binomial Distribution

241

(5)

Appendix 6B. Bayesian Estimation of Failure Fraction, p

246

(4)

Appendix 6C. Weibull Properties

250

(3)

Accelerated Testing

253

(36)

Accelerated Testing

253

(4)

Benefits/Limitations of Accelerated Testing

254

(1)

Two Basic Strategies for Accelerated Testing

255

(2)

Highly Accelerated Life Testing (HALT)

257

(2)

Accelerated Life Test

259

(6)

Accelerated Cycling or Time-Compression Strategies

260

(1)

Stress-Life Relationships at Two Different Stress Levels

260

(5)

Use of Physical Models

265

(9)

The Arrhenius Model

265

(6)

Other Acceleration Models

271

(3)

Use of Linear Statistical Models in Minitab for Evaluating Life Versus Stress Variables Relationships

274

(8)

Arrhenius Linear Model in Minitab

274

(3)

Use of Regression with Life Data Procedure in Minitab

277

(3)

Use of Proportional Hazards Models

280

(2)

Closing Comments

282

(1)

Exercises

282

(7)

Appendix 7A. Q--Q Plots

284

(3)

Appendix 7B. ML Estimation of Parameters in Regression Model with Multiply Censored Life Data

287

(2)

Engineering Approaches to Design Verification

289

(20)

Computer-Aided Engineering Approaches

290

(2)

Finite-Element Analysis

290

(1)

Other Computer-Aided Engineering (CAE) Approaches

291

(1)

Probabilistic Design

292

(8)

Simple Strength Versus Stress Models

292

(3)

Multivariate Strength Versus Stress Competition

295

(5)

Probabilistic FEA

300

(1)

Parametric Models

300

(5)

Summary

305

(1)

Exercises

305

(4)

Appendix 8A. First Order Reliability Method (FORM)

307

(2)

Likelihood Estimation (Advanced)

309

(50)

Maximum Likelihood (ML) Point Estimation

309

(13)

Maximum Likelihood Estimation of Exponential Hazard Parameter, λ

311

(1)

ML Estimates of Normal Parameters, μ and σ2

312

(2)

Worked-Out Example

314

(2)

Weibull Distribution: ML Estimation of β and θ

316

(3)

ML Estimation of Three-Parameter Weibull Distribution

319

(1)

Other Modified Estimation Procedures for the Three-Parameter Weibull Distribution

320

(2)

ML-Based Approaches for Confidence Interval Estimation

322

(29)

Exponential Confidence Intervals

322

(3)

Asymptotic (Large-Sample) Confidence Intervals

325

(4)

Confidence Intervals on Normal Metrics

329

(22)

Exercises

351

(8)

Appendix 9A. Algorithm by Wolynetz (1979) for Obtaining ML Estimates of Normal Parameters, μ and σ

352

(4)

Appendix 9B. Proof: The Exponential Total Unit Time on Test Variable, T, Follows a Gamma (rλ) Distribution

356

(3)

Comparing Designs

359

(20)

Graphical Procedures Based on Probability or Rank Regression Plots

360

(2)

Q--Q Plots

362

(7)

Technical Note: Use of Q--Q Plots

367

(1)

Inferential Statistics for Using Q--Q Plots

368

(1)

Use of Likelihood Theory for Assessing Differences

369

(2)

Approximate F-Test for Differences---Weibull and Exponential Distribution

371

(5)

Test for Differences in the Exponential MTTF Parameter, θ

372

(1)

Approximate Test for Differences with Weibull Shape Parameter

373

(3)

Use of Approximate F-Tests

376

(1)

Summary

376

(1)

Exercises

377

(2)

References

379

(8)

Index

387

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Reliability Verification, Testing, and Analysis in Engineering Design

Summary

Author Biography

Table of Contents

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