Experimental design has been used extensively and successfully to aid in quality achievement; however, there have been fewer successful applications in reliability. Experiments in reliability are inherently different from other industrial experiments since lifetimes usually do not follow a normal distribution, which is often the assumption in experimental design.  Written by internationally known experts in the fields of experimental design methodology and reliability data analysis, this book illustrates how experimental design and tests can improve the reliability of the outcome. Focusing on reliability applications and methods, this book describes and illustrates methods for designing experiments and analyzes the results when the response is a lifetime. This book is organized into four main parts: Part One begins with an introduction to reliability, lifetime distributions, and inference for parameter of lifetime distributions; Part Two focuses on design of experiments, optimal design, and robust design; Part Three features coverage of lifetime regression, parametric regression models, the Cox Proportional Hazard Model, and design strategies for reliability achievement; and Part Four addresses accelerated testing, models for acceleration, and design of experiments for accelerated testing.  The authors also utilize R, SAS®, and JMP® software throughout as appropriate, and a supplemental website contains the related data sets.

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.

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.

Connie M. Borror, PhD, is Professor in the School of Mathematical and Natural Sciences. She is the author of over 70 journal articles and her research interests include design of experiments, statistical quality control, and measurement systems analysis.

Preface xxx

PART I RELIABILITY xxx

1 Reliability Concepts xxx

1.1 Definitions of Reliability xxx

1.2 Concepts for Lifetimes xxx

1.3 Censoring xxx

2 Lifetime Distributions xxx

2.1 The Exponential Distribution xxx

2.2 The Weibull Distribution xxx

2.3 The Gamma Distribution xxx

2.4 The Lognormal Distribution xxx

2.5 Log Location and Scale Distributions xxx

2.5.1 The Smallest Extreme Value Distribution xxx

2.5.2 The Logistic and Log Logistic Distributions xxx

3 Inference for Parameters of Life Distributions xxx

3.1 Nonparametric Estimation of the Survival Function xxx

3.1.1 Confidence Bounds for the Survival Function xxx

3.1.2 Estimating the Hazard Function xxx

3.2 Maximum Likelihood Estimation xxx

3.2.1 Censoring Contributions to Likelihoods xxx

3.3 Inference for the Exponential Distribution xxx

3.3.1 Type II Censoring xxx

3.3.2 Type I Censoring xxx

3.3.3 Arbitrary Censoring xxx

3.3.4 Large Sample Approximations xxx

3.4 Inference for the Weibull xxx

3.5 The SEV Distribution xxx

3.6 Inference for Other Models xxx

3.6.1 Inference for the GAM(_; _) Distribution xxx

3.6.2 Inference for the Log Normal Distribution xxx

3.6.3 Inference for the GGAM(_; _; _) Distribution xxx

3.7 Bayesian Inference xxx

PART II DESIGN OF EXPERIMENTS xxx

4 Fundamentals of Experimental Design xxx

4.1 Introduction to Experimental Design xxx

4.2 A Brief History of Experimental Design xxx

4.3 Guidelines for Designing Experiments xxx

4.4 Introduction to Factorial Experiments xxx

4.4.1 An Example xxx

4.4.2 The Analysis of Variance for a Two Factor Factorial xxx

4.5 The 2k Factorial Design xxx

4.5.1 The 22 Factorial Design xxx

4.5.2 The 23 Factorial Design xxx

4.5.3 A Singe Replicate of the 2k Design xxx

4.5.4 2k Designs are Optimal Designs xxx

4.5.5 Adding Center Runs to a 2k Design xxx

4.6 Fractional Factorial Designs xxx

5 Further Principles of Experimental Design xxx

5.1 Introduction xxx

5.2 Response Surface Methods and Designs xxx

5.3 Optimization Techniques in Response Surface Methodology xxx

5.4 Designs for Fitting Response Surfaces xxx

5.4.1 Classical Response Surface Designs xxx

5.4.2 Definitive Screening Designs xxx

5.4.3 Optimal Designs in RSM xxx

PART III REGRESSION MODELS FOR RELIABILITY STUDIES xxx

6 Parametric Regression Models xxx

6.1 Introduction to Failure Time Regression xxx

6.2 Regression Models with Transformations xxx

6.2.1 Estimations and Confidence Interval for Transformed Data xxx

6.3 Generalized Linear Models xxx

6.4 Incorporating Censoring in Regression Models xxx

6.5 Weibull Regression xxx

6.6 Nonconstant Shape Parameter xxx

6.7 Exponential Regression xxx

6.8 The Scale Accelerated Failure Time Model xxx

6.9 Checking Model Assumptions xxx

6.9.1 Residual Analysis xxx

6.9.2 Distribution Selection xxx

7 Semiparametric Regression Models xxx

7.1 The Proportional Hazards Model xxx

7.2 The Cox Proportional Hazards Model xxx

7.3 Inference for the Cox Proportional Hazards Model xxx

7.4 Checking Assumptions for the Cox PH Model xxx

PART IV EXPERIMENTAL DESIGN FOR RELIABILITY STUDIES xxx

8 Design of Single Testing Condition Reliability Experiments xxx

8.1 Life Testing xxx

8.1.1 Life Test Planning with Exponential Distribution xxx

8.1.2 Life Test Planning for Other Lifetime Distributions xxx

8.1.3 Operating Characteristic Curves xxx

8.2 Accelerated Life Testing xxx

8.2.1 Acceleration Factor xxx

8.2.2 Physical Acceleration Models xxx

8.2.3 Relationship Between Physical Acceleration Models and Statistical Models xxx

8.2.4 Planning Single Stress Level ALTs xxx

9 Design of Multi Factor and Multi Level Reliability Experiments xxx

9.1 Implications of Design for Reliability xxx

9.2 Statistical Acceleration Models xxx

9.2.1 Lifetime regression model xxx

9.2.2 Proportional hazard model xxx

9.2.3 Generalized linear model xxx

9.2.4 Converting PH model with right censoring to GLM xxx

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

9.3.1 Optimal test plans xxx

9.3.2 Locality of Optimal ALT plans xxx

9.3.3 Comparing Optimal ALT Plans xxx

9.4 Bayesian Design for GLM 400 xxx

9.5 Reliability Experiments with Design and Manufacturing Process Variables xxx

Appendices xxx

A The Survival Package in R xxx

B Design of Experiments using JMP xxx

C The Expected Fisher Information Matrix xxx

D Data Sets xxx

E Distributions Used in Life Testing xxx