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Steven E. Rigdon, PhD, is Professor in the Department of Biostatistics at Saint Louis University. He is also Distinguished Research Professor Emeritus at Southern Illinois University Edwardsville. His research interests include spatial disease surveillance and reliability assessment.
Rong Pan, PhD, is Associate Professor of Industrial Engineering at the School of Computing, Informatics, and Decision Systems Engineering at Arizona State University. His research interests include failure time data analysis, design of experiments, multivariate statistical quality control, time series analysis, and control.
Douglas C. Montgomery, PhD, is Regents Professor of Industrial Engineering and ASU Foundation Professor of Engineering at Arizona State University. His research interests include industrial statistics and design of experiments.
Laura J. Freeman, PhD, is Research Associate Professor of Statistics and Director of the Intelligent Systems Division of the National Security Institute at Virginia Tech. Her research interests include design of experiments, leveraging experimental methods in emerging technology research with a focus in cyber-physical systems, artificial intelligence (AI), and machine learning.
Preface xiii
About the Companion Website xv
Part I Reliability 1
1 Reliability Concepts 3
1.1 Definitions of Reliability 3
1.2 Concepts for Lifetimes 4
1.3 Censoring 10
Problems 14
2 Lifetime Distributions 17
2.1 The Exponential Distribution 17
2.2 The Weibull Distribution 22
2.3 The Gamma Distribution 25
2.4 The Lognormal Distribution 28
2.5 Log Location and Scale Distributions 30
2.5.1 The Smallest Extreme Value Distribution 31
2.5.2 The Logistic and Log-Logistic Distributions 33
Problems 35
3 Inference for Parameters of Life Distributions 39
3.1 Nonparametric Estimation of the Survival Function 39
3.1.1 Confidence Bounds for the Survival Function 42
3.1.2 Estimating the Hazard Function 44
3.2 Maximum Likelihood Estimation 46
3.2.1 Censoring Contributions to Likelihoods 46
3.3 Inference for the Exponential Distribution 50
3.3.1 Type II Censoring 50
3.3.2 Type I Censoring 54
3.3.3 Arbitrary Censoring 55
3.3.4 Large Sample Approximations 56
3.4 Inference for the Weibull 58
3.5 The SEV Distribution 59
3.6 Inference for Other Models 60
3.6.1 Inference for the GAM(¿, a) Distribution 61
3.6.2 Inference for the Log Normal Distribution 61
3.6.3 Inference for the GGAM(¿, ¿, a) Distribution 62
3.7 Bayesian Inference 67
3.a Kaplan-Meier Estimate of the Survival Function 80
3.a.1 The Metropolis-Hastings Algorithm 82
Problems 83
Part II Design of Experiments 89
4 Fundamentals of Experimental Design 91
4.1 Introduction to Experimental Design 91
4.2 A Brief History of Experimental Design 93
4.3 Guidelines for Designing Experiments 95
4.4 Introduction to Factorial Experiments 101
4.4.1 An Example 103
4.4.2 The Analysis of Variance for a Two-Factor Factorial 105
4.5 The 2k Factorial Design 114
4.5.1 The 22 Factorial Design 115
4.5.2 The 23 Factorial Design 119
4.5.3 A Singe Replicate of the 2k Design 124
4.5.4 2k Designs are Optimal Designs 129
4.5.5 Adding Center Runs to a 2k Design 133
4.6 Fractional Factorial Designs 135
4.6.1 A General Method for Finding the Alias Relationships in Fractional Factorial Designs 142
4.6.2 De-aliasing Effects 145
Problems 147
5 Further Principles of Experimental Design 157
5.1 Introduction 157
5.2 Response Surface Methods and Designs 157
5.3 Optimization Techniques in Response Surface Methodology 160
5.4 Designs for Fitting Response Surfaces 165
5.4.1 Classical Response Surface Designs 165
5.4.2 Definitive Screening Designs 171
5.4.3 Optimal Designs in RSM 175
Problems 176
Part III Regression Models for Reliability Studies 185
6 Parametric Regression Models 187
6.1 Introduction to Failure-Time Regression 187
6.2 Regression Models with Transformations 188
6.2.1 Estimation and Confidence Intervals for Transformed Data 189
6.3 Generalized Linear Models 198
6.4 Incorporating Censoring in Regression Models 205
6.4.1 Parameter Estimation for Location Scale and Log-Location Scale Models 205
6.4.2 Maximum Likelihood Method for Log-Location Scale Distributions 206
6.4.3 Inference for Location Scale and Log-Location Scale Models 207
6.4.4 Location Scale and Log-Location Scale Regression Models 208
6.5 Weibull Regression 208
6.6 Nonconstant Shape Parameter 228
6.7 Exponential Regression 233
6.8 The Scale-Accelerated Failure-Time Model 234
6.9 Checking Model Assumptions 236
6.9.1 Residual Analysis 237
6.9.2 Distribution Selection 243
Problems 245
7 Semi-parametric Regression Models 249
7.1 The Proportional Hazards Model 249
7.2 The Cox Proportional Hazards Model 251
7.3 Inference for the Cox Proportional Hazards Model 255
7.4 Checking Assumptions for the Cox PH Model 264
Problems 265
Part IV Experimental Design for Reliability Studies 269
8 Design of Single-Testing-Condition Reliability Experiments 271
8.1 Life Testing 272
8.1.1 Life Test Planning with Exponential Distribution 273
8.1.1.1 Type II Censoring 273
8.1.1.2 Type I Censoring 274
8.1.1.3 Large Sample Approximation 275
8.1.1.4 Planning Tests to Demonstrate a Lifetime Percentile 276
8.1.1.5 Zero Failures 279
8.1.2 Life Test Planning for Other Lifetime Distributions 281
8.1.3 Operating Characteristic Curves 282
8.2 Accelerated Life Testing 286
8.2.1 Acceleration Factor 287
8.2.2 Physical Acceleration Models 288
8.2.2.1 Arrhenius Model 288
8.2.2.2 Eyring Model 289
8.2.2.3 Peck Model 290
8.2.2.4 Inverse Power Model 290
8.2.2.5 Coffin-Manson Model 290
8.2.3 Relationship Between Physical Acceleration Models and Statistical Models 291
8.2.4 Planning Single-Stress-Level ALTs 292
Problems 294
9 Design of Multi-Factor and Multi-Level Reliability Experiments 297
9.1 Implications of Design for Reliability 298
9.2 Statistical Acceleration Models 299
9.2.1 Lifetime Regression Model 299
9.2.2 Proportional Hazards Model 303
9.2.3 Generalized Linear Model 306
9.2.4 Converting PH Model with Right Censoring to GLM 309
9.3 Planning ALTs with Multiple Stress Factors at Multiple Stress Levels 311
9.3.1 Optimal Test Plans 313
9.3.2 Locality of Optimal ALT Plans 318
9.3.3 Comparing Optimal ALT Plans 319
9.4 Bayesian Design for GLM 322
9.5 Reliability Experiments with Design and Manufacturing Process Variables 326
Problems 336
A The Survival Package in R 339
B Design of Experiments using JMP 351
C The Expected Fisher Information Matrix 357
C.1 Lognormal Distribution 359
C.2 Weibull Distribution 359
C.3 Lognormal Distribution 361
C.4 Weibull Distribution 362
D Data Sets 363
E Distributions Used in Life Testing 375
Bibliography 381
Index 387
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