Design of Experiments for Reliability Achievement

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 xiiiAbout the Companion Website xvPart I Reliability 11 Reliability Concepts 31.1 Definitions of Reliability 31.2 Concepts for Lifetimes 41.3 Censoring 10Problems 142 Lifetime Distributions 172.1 The Exponential Distribution 172.2 The Weibull Distribution 222.3 The Gamma Distribution 252.4 The Lognormal Distribution 282.5 Log Location and Scale Distributions 302.5.1 The Smallest Extreme Value Distribution 312.5.2 The Logistic and Log-Logistic Distributions 33Problems 353 Inference for Parameters of Life Distributions 393.1 Nonparametric Estimation of the Survival Function 393.1.1 Confidence Bounds for the Survival Function 423.1.2 Estimating the Hazard Function 443.2 Maximum Likelihood Estimation 463.2.1 Censoring Contributions to Likelihoods 463.3 Inference for the Exponential Distribution 503.3.1 Type II Censoring 503.3.2 Type I Censoring 543.3.3 Arbitrary Censoring 553.3.4 Large Sample Approximations 563.4 Inference for the Weibull 583.5 The SEV Distribution 593.6 Inference for Other Models 603.6.1 Inference for the GAM(θ, α) Distribution 613.6.2 Inference for the Log Normal Distribution 613.6.3 Inference for the GGAM(θ, κ, α) Distribution 623.7 Bayesian Inference 673.a Kaplan–Meier Estimate of the Survival Function 803.a.1 The Metropolis–Hastings Algorithm 82Problems 83Part II Design of Experiments 894 Fundamentals of Experimental Design 914.1 Introduction to Experimental Design 914.2 A Brief History of Experimental Design 934.3 Guidelines for Designing Experiments 954.4 Introduction to Factorial Experiments 1014.4.1 An Example 1034.4.2 The Analysis of Variance for a Two-Factor Factorial 1054.5 The 2k Factorial Design 1144.5.1 The 22 Factorial Design 1154.5.2 The 23 Factorial Design 1194.5.3 A Singe Replicate of the 2k Design 1244.5.4 2k Designs are Optimal Designs 1294.5.5 Adding Center Runs to a 2k Design 1334.6 Fractional Factorial Designs 1354.6.1 A General Method for Finding the Alias Relationships in Fractional Factorial Designs 1424.6.2 De-aliasing Effects 145Problems 1475 Further Principles of Experimental Design 1575.1 Introduction 1575.2 Response Surface Methods and Designs 1575.3 Optimization Techniques in Response Surface Methodology 1605.4 Designs for Fitting Response Surfaces 1655.4.1 Classical Response Surface Designs 1655.4.2 Definitive Screening Designs 1715.4.3 Optimal Designs in RSM 175Problems 176Part III Regression Models for Reliability Studies 1856 Parametric Regression Models 1876.1 Introduction to Failure-Time Regression 1876.2 Regression Models with Transformations 1886.2.1 Estimation and Confidence Intervals for Transformed Data 1896.3 Generalized Linear Models 1986.4 Incorporating Censoring in Regression Models 2056.4.1 Parameter Estimation for Location Scale and Log-Location Scale Models 2056.4.2 Maximum Likelihood Method for Log-Location Scale Distributions 2066.4.3 Inference for Location Scale and Log-Location Scale Models 2076.4.4 Location Scale and Log-Location Scale Regression Models 2086.5 Weibull Regression 2086.6 Nonconstant Shape Parameter 2286.7 Exponential Regression 2336.8 The Scale-Accelerated Failure-Time Model 2346.9 Checking Model Assumptions 2366.9.1 Residual Analysis 2376.9.2 Distribution Selection 243Problems 2457 Semi-parametric Regression Models 2497.1 The Proportional Hazards Model 2497.2 The Cox Proportional Hazards Model 2517.3 Inference for the Cox Proportional Hazards Model 2557.4 Checking Assumptions for the Cox PH Model 264Problems 265Part IV Experimental Design for Reliability Studies 2698 Design of Single-Testing-Condition Reliability Experiments 2718.1 Life Testing 2728.1.1 Life Test Planning with Exponential Distribution 2738.1.1.1 Type II Censoring 2738.1.1.2 Type I Censoring 2748.1.1.3 Large Sample Approximation 2758.1.1.4 Planning Tests to Demonstrate a Lifetime Percentile 2768.1.1.5 Zero Failures 2798.1.2 Life Test Planning for Other Lifetime Distributions 2818.1.3 Operating Characteristic Curves 2828.2 Accelerated Life Testing 2868.2.1 Acceleration Factor 2878.2.2 Physical Acceleration Models 2888.2.2.1 Arrhenius Model 2888.2.2.2 Eyring Model 2898.2.2.3 Peck Model 2908.2.2.4 Inverse Power Model 2908.2.2.5 Coffin–Manson Model 2908.2.3 Relationship Between Physical Acceleration Models and Statistical Models 2918.2.4 Planning Single-Stress-Level ALTs 292Problems 2949 Design of Multi-Factor and Multi-Level Reliability Experiments 2979.1 Implications of Design for Reliability 2989.2 Statistical Acceleration Models 2999.2.1 Lifetime Regression Model 2999.2.2 Proportional Hazards Model 3039.2.3 Generalized Linear Model 3069.2.4 Converting PH Model with Right Censoring to GLM 3099.3 Planning ALTs with Multiple Stress Factors at Multiple Stress Levels 3119.3.1 Optimal Test Plans 3139.3.2 Locality of Optimal ALT Plans 3189.3.3 Comparing Optimal ALT Plans 3199.4 Bayesian Design for GLM 3229.5 Reliability Experiments with Design and Manufacturing Process Variables 326Problems 336A The Survival Package in R 339B Design of Experiments using JMP 351C The Expected Fisher Information Matrix 357C.1 Lognormal Distribution 359C.2 Weibull Distribution 359C.3 Lognormal Distribution 361C.4 Weibull Distribution 362D Data Sets 363E Distributions Used in Life Testing 375Bibliography 381Index 387