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El. knyga: Design of Experiments for Reliability Achievement

(Georgia Institute of Technology), , (Southern Illinois University),
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ENABLES READERS TO UNDERSTAND THE METHODS OF EXPERIMENTAL DESIGN TO SUCCESSFULLY CONDUCT LIFE TESTING TO IMPROVE PRODUCT RELIABILITY

This book illustrates how experimental design and life testing can be used to understand product reliability in order to enable reliability improvements. The book is divided into four sections. The first section focuses on statistical distributions and methods for modeling reliability data. The second section provides an overview of design of experiments including response surface methodology and optimal designs. The third section describes regression models for reliability analysis focused on lifetime data. This section provides the methods for how data collected in a designed experiment can be properly analyzed. The final section of the book pulls together all of the prior sections with customized experiments that are uniquely suited for reliability testing. Throughout the text, there is a focus on reliability applications and methods. It addresses both optimal and robust design with censored data.

To aid in reader comprehension, examples and case studies are included throughout the text to illustrate the key factors in designing experiments and emphasize how experiments involving life testing are inherently different. The book provides numerous state-of-the-art exercises and solutions to help readers better understand the real-world applications of experimental design and reliability. The authors utilize R and JMP® software throughout as appropriate, and a supplemental website contains the related data sets.

Written by internationally known experts in the fields of experimental design methodology and reliability data analysis, sample topics covered in the book include:

  • An introduction to reliability, lifetime distributions, censoring, and inference for parameter of lifetime distributions
  • Design of experiments, optimal design, and robust design
  • Lifetime regression, parametric regression models, and the Cox Proportional Hazard Model
  • Design strategies for reliability achievement
  • Accelerated testing, models for acceleration, and design of experiments for accelerated testing

The text features an accessible approach to reliability for readers with various levels of technical expertise. This book is a key reference for statistical researchers, reliability engineers, quality engineers, and professionals in applied statistics and engineering. It is a comprehensive textbook for upper-undergraduate and graduate-level courses in statistics and engineering.

Preface xiii
About the Companion Website xv
Part I Reliability
1(88)
1 Reliability Concepts
3(14)
1.1 Definitions of Reliability
3(1)
1.2 Concepts for Lifetimes
4(6)
1.3 Censoring
10(7)
Problems
14(3)
2 Lifetime Distributions
17(22)
2.1 The Exponential Distribution
17(5)
2.2 The Weibull Distribution
22(3)
2.3 The Gamma Distribution
25(3)
2.4 The Lognormal Distribution
28(2)
2.5 Log Location and Scale Distributions
30(9)
2.5.1 The Smallest Extreme Value Distribution
31(2)
2.5.2 The Logistic and Log-Logistic Distributions
33(2)
Problems
35(4)
3 Inference for Parameters of Life Distributions
39(50)
3.1 Nonparametric Estimation of the Survival Function
39(7)
3.1.1 Confidence Bounds for the Survival Function
42(2)
3.1.2 Estimating the Hazard Function
44(2)
3.2 Maximum Likelihood Estimation
46(4)
3.2.1 Censoring Contributions to Likelihoods
46(4)
3.3 Inference for the Exponential Distribution
50(8)
3.3.1 Type II Censoring
50(4)
3.3.2 Type I Censoring
54(1)
3.3.3 Arbitrary Censoring
55(1)
3.3.4 Large Sample Approximations
56(2)
3.4 Inference for the Weibull
58(1)
3.5 The SEV Distribution
59(1)
3.6 Inference for Other Models
60(7)
3.6.1 Inference for the GAM (θ, α) Distribution
61(1)
3.6.2 Inference for the Log Normal Distribution
61(1)
3.6.3 Inference for the GGAM (θ, κ, α) Distribution
62(5)
3.7 Bayesian Inference
67(13)
3.A Kaplan-Meier Estimate of the Survival Function
80(9)
3.A.1 The Metropolis-Hastings Algorithm
82(1)
Problems
83(6)
Part II Design of Experiments
89(96)
4 Fundamentals of Experimental Design
91(66)
4.1 Introduction to Experimental Design
91(2)
4.2 A Brief History of Experimental Design
93(2)
4.3 Guidelines for Designing Experiments
95(6)
4.4 Introduction to Factorial Experiments
101(13)
4.4.1 An Example
103(2)
4.4.2 The Analysis of Variance for a Two-Factor Factorial
105(9)
4.5 The 2k Factorial Design
114(21)
4.5.1 The 22 Factorial Design
115(4)
4.5.2 The 23 Factorial Design
119(5)
4.5.3 A Singe Replicate of the 2k Design
124(5)
4.5.4 2k Designs are Optimal Designs
129(4)
4.5.5 Adding Center Runs to a 2k Design
133(2)
4.6 Fractional Factorial Designs
135(22)
4.6.1 A General Method for Finding the Alias Relationships in Fractional Factorial Designs
142(3)
4.6.2 De-aliasing Effects
145(2)
Problems
147(10)
5 Further Principles of Experimental Design
157(28)
5.1 Introduction
157(1)
5.2 Response Surface Methods and Designs
157(3)
5.3 Optimization Techniques in Response Surface Methodology
160(5)
5.4 Designs for Fitting Response Surfaces
165(20)
5.4.1 Classical Response Surface Designs
165(6)
5.4.2 Definitive Screening Designs
171(4)
5.4.3 Optimal Designs in RSM
175(1)
Problems
176(9)
Part III Regression Models for Reliability Studies
185(84)
6 Parametric Regression Models
187(62)
6.1 Introduction to Failure-Time Regression
187(1)
6.2 Regression Models with Transformations
188(10)
6.2.1 Estimation and Confidence Intervals for Transformed Data
189(9)
6.3 Generalized Linear Models
198(7)
6.4 Incorporating Censoring in Regression Models
205(3)
6.4.1 Parameter Estimation for Location Scale and Log-Location Scale Models
205(1)
6.4.2 Maximum Likelihood Method for Log-Location Scale Distributions
206(1)
6.4.3 Inference for Location Scale and Log-Location Scale Models
207(1)
6.4.4 Location Scale and Log-Location Scale Regression Models
208(1)
6.5 Weibull Regression
208(20)
6.6 Nonconstant Shape Parameter
228(5)
6.7 Exponential Regression
233(1)
6.8 The Scale-Accelerated Failure-Time Model
234(2)
6.9 Checking Model Assumptions
236(13)
6.9.1 Residual Analysis
237(6)
6.9.2 Distribution Selection
243(2)
Problems
245(4)
7 Semi-parametric Regression Models
249(20)
7.1 The Proportional Hazards Model
249(2)
7.2 The Cox Proportional Hazards Model
251(4)
7.3 Inference for the Cox Proportional Hazards Model
255(9)
7.4 Checking Assumptions for the Cox PH Model
264(5)
Problems
265(4)
Part IV Experimental Design for Reliability Studies
269(112)
8 Design of Single-Testing-Condition Reliability Experiments
271(26)
8.1 Life Testing
272(14)
8.1.1 Life Test Planning with Exponential Distribution
273(1)
8.1.1.1 Type II Censoring
273(1)
8.1.1.2 Type I Censoring
274(1)
8.1.1.3 Large Sample Approximation
275(1)
8.1.1.4 Planning Tests to Demonstrate a Lifetime Percentile
276(3)
8.1.1.5 Zero Failures
279(2)
8.1.2 Life Test Planning for Other Lifetime Distributions
281(1)
8.1.3 Operating Characteristic Curves
282(4)
8.2 Accelerated Life Testing
286(11)
8.2.1 Acceleration Factor
287(1)
8.2.2 Physical Acceleration Models
288(1)
8.2.2.1 Arrhenius Model
288(1)
8.2.2.2 Eyring Model
289(1)
8.2.2.3 Peck Model
290(1)
8.2.2.4 Inverse Power Model
290(1)
8.2.2.5 Coffin-Manson Model
290(1)
8.2.3 Relationship Between Physical Acceleration Models and Statistical Models
291(1)
8.2.4 Planning Single-Stress-Level ALTs
292(2)
Problems
294(3)
9 Design of Multi-Factor and Multi-Level Reliability Experiments
297(84)
9.1 Implications of Design for Reliability
298(1)
9.2 Statistical Acceleration Models
299(12)
9.2.1 Lifetime Regression Model
299(4)
9.2.2 Proportional Hazards Model
303(3)
9.2.3 Generalized Linear Model
306(3)
9.2.4 Converting PH Model with Right Censoring to GLM
309(2)
9.3 Planning ALTs with Multiple Stress Factors at Multiple Stress Levels
311(11)
9.3.1 Optimal Test Plans
313(5)
9.3.2 Locality of Optimal ALT Plans
318(1)
9.3.3 Comparing Optimal ALT Plans
319(3)
9.4 Bayesian Design for GLM
322(4)
9.5 Reliability Experiments with Design and Manufacturing Process Variables
326(13)
Problems
336(3)
A The Survival Package in R
339(12)
B Design of Experiments using JMP
351(6)
C The Expected Fisher Information Matrix
357(6)
C.1 Lognormal Distribution
359(1)
C.2 Weibull Distribution
359(2)
C.3 Lognormal Distribution
361(1)
C.4 Weibull Distribution
362(1)
D Data Sets
363(12)
E Distributions Used in Life Testing
375(6)
Bibliography 381(6)
Index 387
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.
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