Design of Experiments for Reliability Achievement (eBook)

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

2 Lifetime Distributions 17

2.1 The Exponential Distribution 17

2.2 TheWeibull Distribution 22

2.3 The Gamma Distribution 25

2.4 The Lognormal Distribution 28

2.5 Log Location and Scale Distributions 30

3 Inference for Parameters of Life Distributions 39

3.1 Nonparametric Estimation of the Survival Function 39

3.2 Maximum Likelihood Estimation 46

3.3 Inference for the Exponential Distribution 50

3.4 Inference for the Weibull 58

3.5 The SEV Distribution 59

3.6 Inference for Other Models 60

3.7 Bayesian Inference 67

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

4.5 The 2k Factorial Design 114

4.6 Fractional Factorial Designs 135

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

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

6.3 Generalized Linear Models 198

6.4 Incorporating Censoring in Regression Models 205

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

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

Part IV Experimental Design for Reliability Studies 269

8 Design of Single-Testing-Condition Reliability Experiments 271

8.1 Life Testing 272

8.2 Accelerated Life Testing 286

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

9.3 Planning ALTs with Multiple Stress Factors at Multiple Stress Levels 311

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 DataSets 363

E Distributions Used in Life Testing 375

Bibliography 381

Index 387