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An authoritative guide to the most recent advances in statistical methods for quantifying reliability
Statistical Methods for Reliability Data, Second Edition (SMRD2) is an essential guide to the most widely used and recently developed statistical methods for reliability data analysis and reliability test planning. Written by three experts in the area, SMRD2 updates and extends the long- established statistical techniques and shows how to apply powerful graphical, numerical, and simulation-based methods to a range of applications in reliability. SMRD2 is a comprehensive resource that describes maximum likelihood and Bayesian methods for solving practical problems that arise in product reliability and similar areas of application. SMRD2 illustrates methods with numerous applications and all the data sets are available on the book's website. Also, SMRD2 contains an extensive collection of exercises that will enhance its use as a course textbook.
The SMRD2's website contains valuable resources, including R packages, Stan model codes, presentation slides, technical notes, information about commercial software for reliability data analysis, and csv files for the 93 data sets used in the book's examples and exercises. The importance of statistical methods in the area of engineering reliability continues to grow and SMRD2 offers an updated guide for, exploring, modeling, and drawing conclusions from reliability data.
SMRD2 features:
* Contains a wealth of information on modern methods and techniques for reliability data analysis
* Offers discussions on the practical problem-solving power of various Bayesian inference methods
* Provides examples of Bayesian data analysis performed using the R interface to the Stan system based on Stan models that are available on the book's website
* Includes helpful technical-problem and data-analysis exercise sets at the end of every chapter
* Presents illustrative computer graphics that highlight data, results of analyses, and technical concepts
Written for engineers and statisticians in industry and academia, Statistical Methods for Reliability Data, Second Edition offers an authoritative guide to this important topic.
List of contents
Statistical Methods for Reliability Data i
Preface to the Second Edition iii
Preface to First Edition viii
Acknowledgments xii
1 Reliability Concepts and an Introduction to Reliability Data 1
1.1 Introduction 1
1.2 Examples of Reliability Data 3
1.3 General Models for Reliability Data 11
1.4 Models for Time to Event Versus Models for Recurrences in a Sequence of Events 13
1.5 Strategy for Data Collection, Modeling, and Analysis 15
2 Models, Censoring, and Likelihood for Failure-Time Data 19
2.1 Models for Continuous Failure-Time Processes 19
2.2 Models for Discrete Data from a Continuous Process 25
2.3 Censoring 27
2.4 Likelihood 28
3 Nonparametric Estimation for Failure-Time Data 37
3.1 Estimation from Complete Data 38
3.2 Estimation from Singly-Censored Interval Data 38
3.3 Basic Ideas of Statistical Inference 40
3.4 Confidence Intervals from Complete or Singly-Censored Data 41
3.5 Estimation from Multiply-Censored Data 43
3.6 Pointwise Confidence Intervals from Multiply-Censored Data 45
3.7 Estimation from Multiply-Censored Data with Exact Failures 47
3.8 Nonparametric Simultaneous Confidence Bands 49
3.9 Arbitrary Censoring 52
4 Some Parametric Distributions Used in Reliability Applications 60
4.1 Introduction 61
4.2 Quantities of Interest in Reliability Applications 61
4.3 Location-Scale and Log-Location-Scale Distributions 62
4.4 Exponential Distribution 63
4.5 Normal Distribution 64
4.6 Lognormal Distribution 65
4.7 Smallest Extreme Value Distribution 67
4.8 Weibull Distribution 68
4.9 Largest Extreme Value Distribution 70
4.10 Frechet Distribution 71
4.11 Logistic Distribution 73
4.12 Loglogistic Distribution 74
4.13 Generalized Gamma Distribution 75
4.14 Distributions with a Threshold Parameter 76
4.15 Other Methods of Deriving Failure-Time Distributions 78
4.16 Parameters and Parameterization 80
4.17 Generating Pseudorandom Observations from a Specified Distribution 80
5 System Reliability Concepts and Methods 87
5.1 Non-Repairable System Reliability Metrics 88
5.2 Series Systems 88
5.3 Parallel Systems 91
5.4 Series-Parallel Systems 93
5.5 Other System Structures 94
5.6 Multistate System Reliability Models 96
6 Probability Plotting 102
6.1 Introduction 103
6.2 Linearizing Location-Scale-Based Distributions 103
6.3 Graphical Goodness of Fit 105
6.4 Probability Plotting Positions 106
6.5 Notes on the Application of Probability Plotting 111
7 Parametric Likelihood Fitting Concepts: Exponential Distribution 119
7.1 Introduction 120
7.2 Parametric Likelihood 122
7.3 Likelihood Confidence Intervals for theta 123
7.4 Wald (Normal-Approximation) Confidence Intervals for theta 125
7.5 Confidence Intervals for Functions of theta 126
7.6 Comparison of Confidence Interval Procedures 127
7.7 Likelihood for Exact Failure Times 128
7.8 Effect of Sample Size on Confidence Interval Width and the Likelihood Shape 130
7.9 Exponential Distribution Inferences with No Failures 131
8 Maximum Likelihood Estimation for Log-Location-Scale Distributions 138
8.1 Likelihood Definition 139
8.2 Likelihood Confidence Regions and Intervals 142
8.3 Wald Confidence Inter
About the author
William Q. Meeker, PhD, is Professor of Statistics and Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He is a Fellow of the American Association for the Advancement of Science, the American Statistical Association, and the American Society for Quality.
Luis A. Escobar, PhD, is a Professor in the Department of Experimental Statistics at Louisiana State University. He is a Fellow of the American Statistical Association, an elected member of the International Statistics Institute, and an elected Member of the Colombian Academy of Sciences.
Francis G. Pascual, PhD, is an Associate Professor in the Department of Mathematics and Statistics at Washington State University.
Summary
An authoritative guide to the most recent advances in statistical methods for quantifying reliability
Statistical Methods for Reliability Data, Second Edition (SMRD2) is an essential guide to the most widely used and recently developed statistical methods for reliability data analysis and reliability test planning. Written by three experts in the area, SMRD2 updates and extends the long- established statistical techniques and shows how to apply powerful graphical, numerical, and simulation-based methods to a range of applications in reliability. SMRD2 is a comprehensive resource that describes maximum likelihood and Bayesian methods for solving practical problems that arise in product reliability and similar areas of application. SMRD2 illustrates methods with numerous applications and all the data sets are available on the book's website. Also, SMRD2 contains an extensive collection of exercises that will enhance its use as a course textbook.
The SMRD2's website contains valuable resources, including R packages, Stan model codes, presentation slides, technical notes, information about commercial software for reliability data analysis, and csv files for the 93 data sets used in the book's examples and exercises. The importance of statistical methods in the area of engineering reliability continues to grow and SMRD2 offers an updated guide for, exploring, modeling, and drawing conclusions from reliability data.
SMRD2 features:
* Contains a wealth of information on modern methods and techniques for reliability data analysis
* Offers discussions on the practical problem-solving power of various Bayesian inference methods
* Provides examples of Bayesian data analysis performed using the R interface to the Stan system based on Stan models that are available on the book's website
* Includes helpful technical-problem and data-analysis exercise sets at the end of every chapter
* Presents illustrative computer graphics that highlight data, results of analyses, and technical concepts
Written for engineers and statisticians in industry and academia, Statistical Methods for Reliability Data, Second Edition offers an authoritative guide to this important topic.
