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Statistical Methods for Reliability Data 2nd edition [Kõva köide]

(Iowa State University, Ames), (Washington State University), (Louisiana State University)
  • Formaat: Hardback, 704 pages, kõrgus x laius x paksus: 259x183x33 mm, kaal: 1179 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 10-Dec-2021
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118115457
  • ISBN-13: 9781118115459
Teised raamatud teemal:
Statistical Methods for Reliability Data 2nd editionSuurem pilt
  • Formaat: Hardback, 704 pages, kõrgus x laius x paksus: 259x183x33 mm, kaal: 1179 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 10-Dec-2021
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118115457
  • ISBN-13: 9781118115459
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781118115459.html
Märksõnad:
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 books 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.
Preface to the Second Edition xxvii
Preface to the First Edition xxxiii
Acknowledgments xxxvii
1 Reliability Concepts and Reliability Data
1(20)
1.1 Introduction
1(2)
1.1.1 Quality and Reliability
1(1)
1.1.2 Reasons for Collecting Reliability Data
2(1)
1.1.3 Distinguishing Features of Reliability Data
2(1)
1.2 Examples of Reliability Data
3(9)
1.2.1 Failure-Time Data with No Explanatory Variables
4(5)
1.2.2 Failure-Time Data with Explanatory Variables
9(2)
1.2.3 Degradation Data with No Explanatory Variables
11(1)
1.2.4 Degradation Data with Explanatory Variables
12(1)
1.3 General Models for Reliability Data
12(3)
1.3.1 Reliability Studies and Processes
12(1)
1.3.2 Causes of Failure and Degradation Leading to Failure
13(1)
1.3.3 Environmental Effects on Reliability
13(1)
1.3.4 Definition of Time Scale
14(1)
1.3.5 Definitions of Time Origin and Failure Time
14(1)
1.4 Models for Time to Event Versus Sequences of Recurrent Events
15(2)
1.4.1 Modeling Times to an Event
16(1)
1.4.2 Modeling a Sequence of Recurrent Events
16(1)
1.5 Strategy for Data Collection, Modeling, and Analysis
17(4)
1.5.1 Planning a Reliability Study
17(1)
1.5.2 Strategy for Data Analysis and Modeling
17(1)
Bibliographic Notes and Related Topics
18(1)
Exercises
19(2)
2 Models, Censoring, and Likelihood for Failure-Time Data
21(20)
2.1 Models for Continuous Failure-Time Processes
21(6)
2.1.1 Failure-Time Probability Distribution Functions
22(3)
2.1.2 The Quantile Function and Distribution Quantiles
25(1)
2.1.3 Distribution of Remaining Life
25(2)
2.2 Models for Discrete Data from a Continuous Process
27(3)
2.2.1 Multinomial Failure-Time Model
28(1)
2.2.2 Multinomial Failure-Time Model cdf
28(2)
2.3 Censoring
30(1)
2.3.1 Censoring Mechanisms
30(1)
2.3.2 Important Assumptions on Censoring Mechanisms
30(1)
2.3.3 Informative Censoring
31(1)
2.4 Likelihood
31(10)
2.4.1 Likelihood-Based Statistical Methods
31(1)
2.4.2 Specifying the Likelihood Function
31(1)
2.4.3 Contributions to the Likelihood Function
32(2)
2.4.4 Form of the Constant Term C
34(1)
2.4.5 Likelihood Terms for General Reliability Data
35(1)
2.4.6 Other Likelihood Terms
36(1)
Bibliographic Notes and Related Topics
36(1)
Exercises
37(4)
3 Nonparametric Estimation for Failure-Time Data
41(25)
3.1 Estimation from Complete Data
42(1)
3.2 Estimation from Singly-Censored Interval Data
42(2)
3.3 Basic Ideas of Statistical Inference
44(1)
3.3.1 The Sampling Distribution of F(ti)
44(1)
3.3.2 Confidence Intervals
44(1)
3.4 Confidence Intervals from Complete or Singly-Censored Data
45(3)
3.4.1 Pointwise Binomial-Based Conservative Confidence Interval for F(ti)
45(1)
3.4.2 Pointwise Binomial-Based Jeffreys Approximate Confidence Interval for F(ti)
46(1)
3.4.3 Pointwise Wald Approximate Confidence Interval for F(ti)
46(2)
3.5 Estimation from Multiply-Censored Data
48(2)
3.6 Pointwise Confidence Intervals from Multiply-Censored Data
50(4)
3.6.1 Approximate Variance of F(ti)
50(1)
3.6.2 Greenwood's Formula
51(1)
3.6.3 Pointwise Wald Confidence Interval for F(ti)
51(3)
3.7 Estimation from Multiply-Censored Data with Exact Failures
54(1)
3.8 Nonparametric Simultaneous Confidence Bands
54(3)
3.8.1 Motivation
54(1)
3.8.2 Nonparametric Simultaneous Large-Sample Approximate Confidence Bands for F(t)
55(2)
3.8.3 Determining the Time Range for Nonparametric Simultaneous Confidence Bands for F(t)
57(1)
3.9 Arbitrary Censoring
57(9)
Bibliographic Notes and Related Topics
59(1)
Exercises
60(6)
4 Some Parametric Distributions Used in Reliability Applications
66(29)
4.1 Introduction
66(1)
4.2 Quantities of Interest in Reliability Applications
67(1)
4.3 Location-Scale and Log-Location-Scale Distributions
68(1)
4.4 Exponential Distribution
69(1)
4.4.1 CDF, PDF, Moments, HF, and Quantile Functions
69(1)
4.4.2 Motivation and Applications
69(1)
4.5 Normal Distribution
70(2)
4.5.1 CDF, PDF, Moments, and Quantile Function
70(1)
4.5.2 Motivation and Applications
71(1)
4.6 Lognormal Distribution
72(1)
4.6.1 CDF, PDF, Moments, and Quantile Function
72(1)
4.6.2 Motivation and Applications
73(1)
4.7 Smallest Extreme Value Distribution
73(1)
4.7.1 CDF, PDF, Moments, HF, and Quantile Functions
73(1)
4.7.2 Motivation and Applications
74(1)
4.8 Weibull Distribution
74(2)
4.8.1 CDF, Moments, and Quantile Function
74(1)
4.8.2 Alternative Parameterization
75(1)
4.8.3 Alternative Parameterization CDF, PDF, HF, and Quantile Function
76(1)
4.8.4 Motivation and Applications
76(1)
4.9 Largest Extreme Value Distribution
76(1)
4.9.1 CDF, PDF, Moments, HF, and Quantile Function
76(1)
4.9.2 Motivation and Applications
77(1)
4.10 Frechet Distribution
77(2)
4.10.1 CDF, Moments, and Quantile Function
77(1)
4.10.2 Alternative Parameterization
78(1)
4.10.3 CDF, PDF, and Quantile Function in the Alternative Parameterization
79(1)
4.10.4 Motivation and Applications
79(1)
4.11 Logistic Distribution
79(1)
4.11.1 CDF, PDF, Moments, and Quantile Function
79(1)
4.11.2 Similarity to the Normal Distribution
80(1)
4.12 Loglogistic Distribution
80(2)
4.12.1 CDF and PDF
80(1)
4.12.2 Moments and Quantile Function
81(1)
4.12.3 Motivation and Applications
81(1)
4.13 Generalized Gamma Distribution
82(1)
4.13.1 CDF and PDF
82(1)
4.13.2 Moments and Quantile Function
82(1)
4.13.3 Special Cases of the Generalized Gamma Distribution
83(1)
4.14 Distributions with a Threshold Parameter
83(1)
4.15 Other Methods of Deriving Failure-Time Distributions
84(3)
4.15.1 Discrete Mixture Distributions
85(1)
4.15.2 Continuous Mixture Distributions
85(1)
4.15.3 Power Distributions
86(1)
4.16 Parameters and Parameterization
87(1)
4.17 Generating Pseudorandom Observations from a Specified Distribution
87(8)
4.17.1 Uniform Pseudorandom Number Generator
87(1)
4.17.2 Pseudorandom Observations from Continuous Distributions
88(1)
4.17.3 Efficient Generation of Pseudorandom Censored Samples
88(1)
4.17.4 Pseudorandom Observations from Discrete Distributions
89(1)
Bibliographic Notes and Related Topics
89(1)
Exercises
90(5)
5 System Reliability Concepts and Methods
95(16)
5.1 Nonrepairable System Reliability Metrics
96(1)
5.1.1 System cdf
96(1)
5.1.2 Other Nonrepairable System Reliability Metrics
96(1)
5.2 Series Systems
96(3)
5.2.1 Probability of Failure for a Series System Having Components with Independent Failure Times
96(1)
5.2.2 Importance of Part Count in Product Design
97(1)
5.2.3 Series System of Independent Components Having Weibull Distributions with the Same Shape Parameter
98(1)
5.2.4 Effect of Positive Dependency in a Two-Component Series System
98(1)
5.3 Parallel Systems
99(2)
5.3.1 The Effect of Parallel Redundancy in Improving (Sub)System Reliability
100(1)
5.3.2 Effect of Positive Dependency in a Two-Component Parallel-Redundant System
100(1)
5.3.3 Another Kind of Redundancy
101(1)
5.4 Series-Parallel Systems
101(2)
5.4.1 Series-Parallel Systems with System-Level Redundancy
102(1)
5.4.2 Series-Parallel System Structure with Component-Level Redundancy
102(1)
5.5 Other System Structures
103(1)
5.5.1 Bridge-System Structures
103(1)
5.5.2 k-out-of-m System Structure
103(1)
5.5.3 k-out-of-m: F (Failed) Systems
104(1)
5.6 Multistate System Reliability Models
104(7)
5.6.1 Nonrepairable Multistate Systems
105(1)
5.6.2 Repairable Multistate Systems
105(1)
5.6.3 Repairable System Availability
105(1)
5.6.4 Repairable System and Mean Time between Failures
106(1)
Bibliographic Notes and Related Topics
106(1)
Exercises
107(4)
6 Probability Plotting
111(18)
6.1 Introduction
112(1)
6.2 Linearizing Location-Scale-Based Distributions
112(2)
6.2.1 Linearizing the Exponential Distribution cdf
112(1)
6.2.2 Linearizing the Normal Distribution cdf
112(1)
6.2.3 Linearizing the Lognormal Distribution cdf
113(1)
6.2.4 Linearizing the Weibull Distribution cdf
113(1)
6.2.5 Linearizing the cdf of Other Location-Scale or Log-Location-Scale Distributions
114(1)
6.3 Graphical Goodness of Fit
114(1)
6.4 Probability Plotting Positions
115(6)
6.4.1 Criteria for Choosing Plotting Positions
115(1)
6.4.2 Choice of Plotting Positions
116(4)
6.4.3 Summary of Probability Plotting Methods
120(1)
6.5 Notes on the Application of Probability Plotting
121(8)
6.5.1 Using Simulation to Help Interpret Probability Plots
121(1)
6.5.2 Possible Reason for a Bend in a Probability Plot
122(3)
Bibliographic Notes and Related Topics
125(1)
Exercises
126(3)
7 Parametric Likelihood Fitting Concepts: Exponential Distribution
129(21)
7.1 Introduction
130(2)
7.1.1 Maximum Likelihood Background
130(1)
7.1.2 Model Selection
131(1)
7.2 Parametric Likelihood
132(2)
7.2.1 Probability of the Data
132(1)
7.2.2 Likelihood Function and its Maximum
133(1)
7.3 Likelihood Confidence Intervals for θ
134(2)
7.3.1 Confidence Intervals Based on a Profile Likelihood
134(1)
7.3.2 Relationship between Confidence Intervals and Significance Tests
135(1)
7.4 Wald (Normal-Approximation) Confidence Intervals for θ
136(2)
7.5 Confidence Intervals for Functions of θ
138(1)
7.5.1 Confidence Intervals for the Arrival Rate
138(1)
7.5.2 Confidence Intervals for F(t; θ)
138(1)
7.6 Comparison of Confidence Interval Procedures
139(1)
7.7 Likelihood for Exact Failure Times
139(2)
7.7.1 Correct Likelihood for Observations Reported as Exact Failures
139(1)
7.7.2 Using the Density Approximation for Observations Reported as Exact Failures
139(1)
7.7.3 ML Estimates for the Exponential Distribution θ Based on the Density Approximation
140(1)
7.7.4 Confidence Intervals for the Exponential Distribution with Complete Data or Type 2 (Failure) Censoring
140(1)
7.8 Effect of Sample Size on Confidence Interval Width and the Likelihood Shape
141(2)
7.8.1 Effect of Sample Size on Confidence Interval Width
141(1)
7.8.2 Effect of Sample Size on the Likelihood Shape
142(1)
7.9 Exponential Distribution Inferences with no Failures
143(7)
Bibliographic Notes and Related Topics
145(1)
Exercises
146(4)
8 Maximum Likelihood Estimation for Log-Location-Scale Distributions
150(28)
8.1 Likelihood Definition
151(3)
8.1.1 The Likelihood for Location-Scale Distributions
151(1)
8.1.2 The Likelihood for Log-Location-Scale Distributions
151(3)
8.1.3 Akaike Information Criterion
154(1)
8.2 Likelihood Confidence Regions and Intervals
154(5)
8.2.1 Joint Confidence Regions for μ and σ
154(1)
8.2.2 Likelihood Confidence Intervals for μ
155(1)
8.2.3 Likelihood Confidence Intervals for σ
155(1)
8.2.4 Likelihood Confidence Intervals for Functions of μ and σ
156(2)
8.2.5 Relationship between Confidence Intervals and Significance Tests
158(1)
8.3 Wald Confidence Intervals
159(6)
8.3.1 Variance-Covariance Matrix of Parameter Estimates
159(1)
8.3.2 Wald Confidence Intervals for Model Parameters
160(2)
8.3.3 Wald Confidence Intervals for Functions of μ and σ
162(3)
8.4 The ML Estimate may not go Through the Points
165(1)
8.5 Estimation with a Given Shape Parameter
166(12)
8.5.1 Estimation for a Weibull/Smallest Extreme Value Distribution with Given a
166(2)
8.5.2 Estimation for a Weibull/Smallest Extreme Value Distribution with Given β = 1/σ and Zero Failures
168(2)
Bibliographic Notes and Related Topics
170(1)
Exercises
171(7)
9 Parametric Bootstrap and Other Simulation-Based Confidence Interval Methods
178(28)
9.1 Introduction
179(1)
9.1.1 Motivation
179(1)
9.1.2 Basic Concepts
179(1)
9.2 Methods for Generating Bootstrap Samples and Obtaining Bootstrap Estimates
180(6)
9.2.1 Bootstrap Resampling
180(1)
9.2.2 Fractional-Random-Weight Bootstrap Sampling
181(2)
9.2.3 Parametric Bootstrap Samples and Bootstrap Estimates
183(1)
9.2.4 How to Choose Which Bootstrap Sampling Method to Use
184(1)
9.2.5 Choosing the Number of Bootstrap Samples
185(1)
9.3 Bootstrap Confidence Interval Methods
186(6)
9.3.1 Calculation of Quantiles of a Bootstrap Distribution
186(1)
9.3.2 The Simple Percentile Method
187(1)
9.3.3 The BC Percentile Method
188(1)
9.3.4 The Bootstrap-t Method
189(3)
9.4 Bootstrap Confidence Intervals Based on Pivotal Quantities
192(5)
9.4.1 Introduction
192(1)
9.4.2 Pivotal Quantity Confidence Intervals for the Location Parameter of a Location-Scale Distribution or the Scale Parameter of a Log-Location-Scale Distribution
193(2)
9.4.3 Pivotal Quantity Confidence Intervals for the Scale Parameter of a Location-Scale Distribution or the Shape Parameter of a Log-Location-Scale Distribution
195(1)
9.4.4 Pivotal Quantity Confidence Intervals for the p Quantile of a Location-Scale or a Log-Location-Scale Distribution
196(1)
9.5 Confidence Intervals Based on Generalized Pivotal Quantities
197(9)
9.5.1 Generalized Pivotal Quantities for μ and σ of a Location-Scale Distribution and for Functions of μ and σ
198(1)
9.5.2 Confidence Intervals for Tail Probabilities for (Log-)Location-Scale Distributions
199(1)
9.5.3 Confidence Intervals for the Mean of a Log-Location-Scale Distribution
200(2)
Bibliographic Notes and Related Topics
202(1)
Exercises
203(3)
10 An Introduction to Bayesian Statistical Methods for Reliability
206(33)
10.1 Bayesian Inference: Overview
207(4)
10.1.1 Motivation
207(1)
10.1.2 The Relationship between Non-Bayesian Likelihood Inference and Bayesian Inference
207(1)
10.1.3 Bayes' Theorem and Bayesian Data Analysis
208(1)
10.1.4 The Need for Prior Information
209(1)
10.1.5 Parameterization
209(2)
10.2 Bayesian Inference: An Illustrative Example
211(9)
10.2.1 Specification of Prior Information
211(2)
10.2.2 Characterizing the Joint Posterior Distribution via Simulation
213(1)
10.2.3 Comparison of Joint Posterior Distributions Based on Weakly Informative and Informative Prior Information on the Weibull Shape Parameter (3
213(2)
10.2.4 Generating Sample Draws via Simple Simulation
215(1)
10.2.5 Using the Sample Draws to Construct Bayesian Point Estimates and Credible Intervals
215(5)
10.3 More About Prior Information and Specification of a Prior Distribution
220(4)
10.3.1 Noninformative Prior Distributions
220(1)
10.3.2 Weakly Informative and Informative Prior Distributions
221(1)
10.3.3 Using a Range to Specify a Prior Distribution
222(1)
10.3.4 Whose Prior Distribution Should We Use?
223(1)
10.3.5 Sources of Prior Information
223(1)
10.4 Implementing Bayesian Analyses Using MCMC Simulation
224(5)
10.4.1 Basic Ideas of MCMC Simulation
224(1)
10.4.2 Risks of Misuse and Diagnostics
225(2)
10.4.3 MCMC Summary
227(1)
10.4.4 Software for MCMC
228(1)
10.5 Using Prior Information to Estimate the Service-Life Distribution of a Rocket Motor
229(10)
10.5.1 Background
229(2)
10.5.2 Rocket-Motor Prior Information
231(1)
10.5.3 Rocket-Motor Bayesian Estimation Results
231(1)
10.5.4 Credible Interval for the Proportion of Healthy Rocket Motors after 20 or 30 Years in the Stockpile
232(1)
Bibliographic Notes and Related Topics
233(2)
Exercises
235(4)
11 Special Parametric Models
239(28)
11.1 Extending Maximum Likelihood Methods
239(1)
11.1.1 Likelihood for Other Distributions and Models
239(1)
11.1.2 Confidence Intervals for Other Distributions and Models
240(1)
11.2 Fitting the Generalized Gamma Distribution
240(4)
11.3 Fitting the Birnbaum--Saunders Distribution
244(2)
11.3.1 Birnbaum--Saunders Distribution
244(1)
11.3.2 Birnbaum--Saunders ML Estimation
244(2)
11.4 The Limited Failure Population Model
246(1)
11.4.1 The LFP Likelihood Function and Its Maximum
246(1)
11.4.2 Profile Likelihood Functions and LR-Based Confidence Intervals for μ, σ, and p
246(1)
11.5 Truncated Data and Truncated Distributions
247(8)
11.5.1 Examples of Left Truncation
248(2)
11.5.2 Likelihood with Left Truncation
250(1)
11.5.3 Nonparametric Estimation with Left Truncation
250(1)
11.5.4 ML Estimation with Left-Truncated Data
251(1)
11.5.5 Examples of Right Truncation
252(1)
11.5.6 Likelihood with Right (and Left) Truncation
253(1)
11.5.7 Nonparametric Estimation with Right (and Left) Truncation
253(1)
11.5.8 A Trick to Handle Truncated Observations
254(1)
11.6 Fitting Distributions that Have a Threshold Parameter
255(12)
11.6.1 Estimation with a Given Threshold Parameter
255(1)
11.6.2 Probability Plotting Methods
255(1)
11.6.3 Likelihood Methods
256(3)
11.6.4 Summary of Results of Fitting Models to Skewed Distributions
259(3)
Bibliographic Notes and Related Topics
262(1)
Exercises
263(4)
12 Comparing Failure-Time Distributions
267(22)
12.1 Background and Motivation
267(1)
12.1.1 Reasons for Comparing Failure-Time Distributions
267(1)
12.1.2 Motivating Examples
268(1)
12.2 Nonparametric Comparisons
268(3)
12.2.1 Graphical Nonparametric Comparisons
268(1)
12.2.2 Nonparametric Comparison Tests
268(3)
12.3 Parametric Comparison of Two Groups by Fitting Separate Distributions
271(3)
12.4 Parametric Comparison of Two Groups by Fitting Separate Distributions with Equal σ Values
274(2)
12.5 Parametric Comparison of More than Two Groups
276(13)
12.5.1 Comparison Using Separate Analyses
276(1)
12.5.2 Comparison Using Equal-σ Values
276(3)
12.5.3 Comparison Using Simultaneous Confidence Intervals
279(5)
Bibliographic Notes and Related Topics
284(1)
Exercises
284(5)
13 Planning Life Tests for Estimation
289(23)
13.1 Introduction
289(2)
13.1.1 Basic Ideas
289(2)
13.2 Simple Formulas to Determine the Sample Size Needed
291(5)
13.2.1 Motivation for Use of Large-Sample Approximations of Test Plan Properties
291(1)
13.2.2 Estimating an Unrestricted Quantile and Other Unrestricted Quantities
292(1)
13.2.3 Plots of Quantile Variance Factors
292(2)
13.2.4 Sample Size Formula for Estimating an Unrestricted Quantile and Other Unrestricted Quantities
294(1)
13.2.5 Estimating a Positive Quantile and Other Positive Quantities
294(1)
13.2.6 Sample Size Formula for Estimating a Positive Quantile and Other Positive Quantities
295(1)
13.2.7 Meeting the Precision Criterion
295(1)
13.3 Use of Simulation in Test Planning
296(7)
13.3.1 Basic Idea
296(1)
13.3.2 Assessing the Effect of Test Length on Precision
296(6)
13.3.3 Assessing the Tradeoff between Sample Size and Test Length
302(1)
13.3.4 Uncertainty in Planning Values
302(1)
13.4 Approximate Variance of ML Estimators and Computing Variance Factors
303(1)
13.4.1 A General Large-Sample Approximation for the Variances of ML Estimators
303(1)
13.4.2 A General Large-Sample Approximation for the Variance of the ML Estimator of a Function of the Parameters
303(1)
13.5 Variance Factors for (Log-)Location-Scale Distributions
304(3)
13.5.1 Large-Sample Approximate Variance-Covariance Matrix for Location-Scale Parameters
304(1)
13.5.2 Variance Factors for (Log-)Location-Scale Distribution Parameter Estimators
305(1)
13.5.3 Variance Factors for Functions of (Log-)Location-Scale Distribution Parameter Estimators
306(1)
13.5.4 Variance Factors to Estimate a Quantile When T is Log-Location-Scale
306(1)
13.6 Some Extensions
307(5)
13.6.1 Type 2 (Failure) Censoring
307(1)
13.6.2 Variance Factors for Location-Scale Parameters and Multiple Censoring
308(1)
13.6.3 Test Planning for Distributions that Are Not Log-Location-Scale
308(1)
Bibliographic Notes and Related Topics
308(1)
Exercises
309(3)
14 Planning Reliability Demonstration Tests
312(11)
14.1 Introduction to Demonstration Testing
312(2)
14.1.1 Criteria for Doing a Demonstration
312(1)
14.1.2 Basic Ideas of Demonstration Testing
313(1)
14.1.3 Data and Distribution
313(1)
14.1.4 The Important Relationship between S(td) and S(tc)
313(1)
14.1.5 The Demonstration Test Decision Rule
314(1)
14.2 Finding the Required Sample Size or Test-Length Factor
314(4)
14.2.1 Required Sample Size n for a Given Test-Length Factor k
314(1)
14.2.2 Required Test-Length Factor k for a Given Sample Size n
314(1)
14.2.3 Minimum-Sample-Size Test
314(1)
14.2.4 Minimum-Sample-Size Test for the Weibull Distribution
315(3)
14.3 Probability of Successful Demonstration
318(5)
14.3.1 General Approach
318(1)
14.3.2 Special Result for the Weibull Minimum-Sample-Size Test
319(1)
Bibliographic Notes and Related Topics
320(1)
Exercises
321(2)
15 Prediction of Failure Times and the Number of Future Field Failures
323(32)
15.1 Basic Concepts of Statistical Prediction
324(1)
15.1.1 Motivation and Prediction Applications
324(1)
15.1.2 What is Needed to Compute a Prediction Interval?
325(1)
15.2 Probability Prediction Intervals (θ Known)
325(1)
15.3 Statistical Prediction Interval (θ Estimated)
326(2)
15.3.1 Coverage Probability Concepts
326(1)
15.3.2 Relationship between One-Sided Prediction Bounds and Two-Sided Prediction Intervals
327(1)
15.3.3 Prediction Based on a Pivotal Quantity
327(1)
15.4 Plug-In Prediction and Calibration
328(4)
15.4.1 The Plug-in Method for Computing an Approximate Statistical Prediction Interval
328(1)
15.4.2 Calibrating Plug-in Statistical Prediction Bounds
329(1)
15.4.3 The Calibration-Bootstrap Prediction Method
330(1)
15.4.4 Finding a Calibration Curve by Computing Coverage Probabilities for the Plug-in Method
330(2)
15.4.5 Assessing the Amount of Monte Carlo Error
332(1)
15.5 Computing and Using Predictive Distributions
332(4)
15.5.1 Definition and Use of a Predictive Distribution
332(1)
15.5.2 A Simple Method for Computing a Predictive Distribution
333(1)
15.5.3 Alternative Methods for Computing a Predictive Distribution
333(2)
15.5.4 A General Alternative Method of Computing Prediction Intervals Using the Calibration Bootstrap and an Extra Layer of Simulation
335(1)
15.6 Prediction of the Number of Future Failures from a Single Group
336(2)
15.6.1 Problem Background
336(1)
15.6.2 Distribution of the Predictand, Point Prediction, and the Plug-in Prediction Method
336(1)
15.6.3 Correcting the Plug-in Method
337(1)
15.7 Predicting the Number of Future Failures from Multiple Groups
338(5)
15.7.1 Distribution of the Number of Future Failures
339(1)
15.7.2 Plug-in Prediction Bounds and Intervals for the Number of Future Failures
340(2)
15.7.3 Approximations for the Poisson-Binomial Distribution
342(1)
15.7.4 Improved Prediction Bounds and Intervals for the Number of Future Failures
342(1)
15.8 Bayesian Prediction Methods
343(2)
15.8.1 Motivation for the Use of Bayesian Prediction Methods
343(1)
15.8.2 Computing a Bayesian Predictive Distribution
344(1)
15.9 Choosing a Distribution for Making Predictions
345(10)
Bibliographic Notes and Related Topics
346(2)
Exercises
348(7)
16 Analysis of Data with More than One Failure Mode
355(22)
16.1 An Introduction to Multiple Failure Modes
355(2)
16.1.1 Basic Idea
355(1)
16.1.2 Multiple Failure Modes Data
356(1)
16.2 Model for Multiple Failure Modes Data
357(2)
16.2.1 Association between Failure Times of Different Failure Modes
357(1)
16.2.2 The Assumption of Independence
358(1)
16.2.3 System Failure-Time Distribution with All Failure Modes Active
358(1)
16.3 Multiple Failure Modes Estimation
359(4)
16.3.1 Maximum Likelihood Estimation with Multiple Failure Modes
359(4)
16.3.2 Importance of Accounting for Failure-Mode Information
363(1)
16.4 The Effect of Eliminating a Failure Mode
363(3)
16.5 Subdistribution Functions and Prediction for Individual Failure Modes
366(2)
16.5.1 Subdistribution Functions
366(1)
16.5.2 Predictions for Individual Failure Modes
367(1)
16.6 More About the Nonidentifiability of Dependence Among Failure Modes
368(9)
Bibliographic Notes and Related Topics
369(1)
Exercises
370(7)
17 Failure-Time Regression Analysis
377(32)
17.1 Introduction
378(1)
17.1.1 Motivating Example
378(1)
17.1.2 Failure-Time Regression Models
378(1)
17.2 Simple Linear Regression Models
379(3)
17.2.1 Location-Scale Regression Model and Likelihood
379(1)
17.2.2 Log-Location-Scale Regression Model and Likelihood
380(2)
17.3 Standard Errors and Confidence Intervals for Regression Models
382(3)
17.3.1 Standard Errors and Confidence Intervals for Parameters
382(1)
17.3.2 Standard Errors and Confidence Intervals for Distribution Quantities at Specific Explanatory Variable Conditions
383(2)
17.4 Regression Model with Quadratic μ and Nonconstant σ
385(4)
17.4.1 Quadratic Regression Relationship for μ and a Constant σ Parameter
386(1)
17.4.2 Quadratic Regression Model with Nonconstant Shape Parameter σ
387(1)
17.4.3 Further Comments on the Use of Empirical Regression Models
388(1)
17.4.4 Comments on Numerical Methods and Parameterization
388(1)
17.5 Checking Model Assumptions
389(3)
17.5.1 Definition of Residuals
389(1)
17.5.2 Cox-Snell Residuals
390(1)
17.5.3 Regression Diagnostics
391(1)
17.6 Empirical Regression Models and Sensitivity Analysis
392(5)
17.7 Models with Two or More Explanatory Variables
397(12)
17.7.1 Model-Free Graphical Analysis of Two-Variable Regression Data
398(1)
17.7.2 Two-Variable Regression Model without Interaction
399(1)
17.7.3 Two-Variable Regression Model with Interaction
400(3)
Bibliographic Notes and Related Topics
403(1)
Exercises
404(5)
18 Analysis of Accelerated Life-Test Data
409(29)
18.1 Introduction to Accelerated Life Tests
409(2)
18.1.1 Motivation and Background for Accelerated Testing
409(1)
18.1.2 Different Methods of Acceleration
410(1)
18.2 Overview of ALT Data Analysis Methods
411(1)
18.2.1 ALT Models
411(1)
18.2.2 Strategy for Analyzing ALT Data
412(1)
18.3 Temperature-Accelerated Life Tests
412(9)
18.3.1 Introduction
412(1)
18.3.2 Scatterplot of ALT Data
413(3)
18.3.3 The Arrhenius Acceleration Model
416(2)
18.3.4 Checking Other Model Assumptions
418(1)
18.3.5 ML Estimates at Use Conditions
419(2)
18.4 Bayesian Analysis of a Temperature-Accelerated Life Test
421(2)
18.4.1 Introduction
421(1)
18.4.2 Parameterization of the Arrhenius Model
421(1)
18.4.3 Prior Distribution Specification in an ALT
422(1)
18.4.4 Bayesian Analysis of the Device-A ALT Data
422(1)
18.5 Voltage-Accelerated Life Test
423(15)
18.5.1 Voltage and Voltage-Stress Acceleration
424(1)
18.5.2 The Inverse-Power Relationship
425(5)
18.5.3 ML Estimates at Use Conditions for the M-P Insulation
430(1)
18.5.4 Physical Motivation for the Inverse-Power Relationship for Voltage-Stress Acceleration
430(1)
18.5.5 A Generalization of the Inverse-Power Relationship
431(1)
Bibliographic Notes and Related Topics
432(1)
Exercises
433(5)
19 More Topics on Accelerated Life Testing
438(27)
19.1 Accelerated Life Tests with Interval-Censored Data
438(6)
19.1.1 Maximum Likelihood Estimation at Individual Test Conditions
439(2)
19.1.2 ML Estimates of the Arrhenius-Lognormal Model Parameters with Interval-Censored Data
441(1)
19.1.3 Fitting an ALT Model with a Given Relationship Slope
442(1)
19.1.4 Bayesian Analysis of Interval-Censored ALT Data
442(2)
19.2 Accelerated Life Tests with Two Accelerating Variables
444(4)
19.3 Multifactor Experiments with a Single Accelerating Variable
448(4)
19.4 Practical Suggestions for Drawing Conclusions from ALT Data
452(2)
19.4.1 Predicting Product Performance
452(1)
19.4.2 Drawing Conclusions from ALTs
453(1)
19.4.3 Planning ALTs
453(1)
19.5 Pitfalls of Accelerated Life Testing
454(2)
19.5.1 Pitfall: Extraneous Failure Modes Caused by Too Much Acceleration
454(1)
19.5.2 Pitfall: Masked Failure Modes
455(1)
19.5.3 Pitfall: Faulty Comparison
455(1)
19.6 Other Kinds of Accelerated Tests
456(9)
19.6.1 Accelerated Tests with Step-Stress and Varying Stress
456(1)
19.6.2 Continuous Product Operation to Accelerate Testing
457(1)
19.6.3 Qualitative Accelerated Life Tests
458(1)
19.6.4 Burn-in
459(1)
Bibliographic Notes and Related Topics
459(2)
Exercises
461(4)
20 Degradation Modeling and Destructive Degradation Data Analysis
465(31)
20.1 Degradation Reliability Data and Degradation Path Models: Introduction and Background
466(2)
20.1.1 Motivation
466(1)
20.1.2 Examples of Degradation Data
466(1)
20.1.3 Limitations of Degradation Data
467(1)
20.2 Description and Mechanistic Motivation for Degradation Path Models
468(3)
20.2.1 Shapes of Degradation Paths
468(1)
20.2.2 A Statistical Model for Degradation Data without Explanatory Variables
469(1)
20.2.3 A Statistical Model for Degradation Data with Explanatory Variables
470(1)
20.2.4 Degradation Path Models
470(1)
20.3 Models Relating Degradation and Failure
471(1)
20.3.1 Soft Failures: Specified Degradation Level
471(1)
20.3.2 Hard Failures: Joint Distribution of Degradation and Failure Level
472(1)
20.4 DDT Background, Motivating Examples, and Estimation
472(5)
20.4.1 Background
472(1)
20.4.2 Motivating Examples
472(2)
20.4.3 Transformations for ADDT Data
474(1)
20.4.4 Fitting a Statistical Model to ADDT Data
474(1)
20.4.5 Degradation Model Checking
475(2)
20.5 Failure-Time Distributions Induced from DDT Models and Failure-Time Inferences
477(2)
20.5.1 A General Approach to Obtaining the Failure-Time Distribution for DDT Models
477(1)
20.5.2 Failure-Time Inferences for Model 2
478(1)
20.6 ADDT Model Building
479(2)
20.6.1 Transformations for ADDT Data 4
79(400)
20.6.2 Fitting Separate Models to the Different Levels of the Accelerating Variable
479(2)
20.7 Fitting an Acceleration Model to ADDT Data
481(2)
20.7.1 A Model and Likelihood for ADDT Data
481(1)
20.7.2 ADDT Model Checking
482(1)
20.8 ADDT Failure-Time Inferences
483(2)
20.8.1 Failure-Time cdf for Model 6
483(2)
20.8.2 Failure-Time Distribution Quantiles for Model 6
485(1)
20.9 ADDT Analysis Using an Informative Prior Distribution
485(2)
20.10 An ADDT with an Asymptotic Model
487(9)
20.10.1 ADDT Data with an Asymptote
487(1)
20.10.2 Finding a Model for ADDT Data with an Asymptote
488(1)
20.10.3 Fitting an ADDT Model with an Asymptote
489(1)
20.10.4 ADDT Model Checking with an Asymptotic Model
489(1)
20.10.5 Failure-Time cdf for Model 8
490(1)
20.10.6 Failure-Time Distribution Quantiles for Model 8
491(1)
Bibliographic Notes and Related Topics
492(1)
Exercises
493(3)
21 Repeated-Measures Degradation Modeling and Analysis
496(26)
21.1 RMDT Models and Data
496(4)
21.1.1 RMDT Motivating Example
497(1)
21.1.2 Repeated-Measures Degradation Models
498(1)
21.1.3 Models for Variation in Degradation and Failure Times
498(2)
21.2 RMDT Parameter Estimation
500(3)
21.2.1 RMDT Models with Random Parameters
500(1)
21.2.2 The Likelihood for Random-Parameter Models
501(1)
21.2.3 Bayesian Estimation with Random Parameters
501(2)
21.2.4 RMDT Modeling and Diagnostics
503(1)
21.3 The Relationship between Degradation and Failure Time for RMDT Models
503(4)
21.3.1 Time-to-First-Crossing Distribution
503(1)
21.3.2 A General Approach
504(1)
21.3.3 Analytical Solution for F(t)
504(2)
21.3.4 Numerical Evaluation of F(t)
506(1)
21.3.5 Monte Carlo Evaluation of F(t)
506(1)
21.4 Estimation of a Failure-Time CDF from RMDT Data
507(1)
21.5 Models for ARMDT Data
508(1)
21.6 ARMDT Estimation
509(4)
21.6.1 Estimation of Failure Probabilities, Distribution Quantiles, and Other Functions of Model Parameters for an ARMDT Model
510(1)
21.6.2 ARMDT Analysis Using an Informative Prior Distribution
511(2)
21.7 ARMDT with Multiple Accelerating Variables
513(9)
Bibliographic Notes and Related Topics
515(2)
Exercises
517(5)
22 Analysis of Repairable System and Other Recurrent Events Data
522(15)
22.1 Introduction
522(2)
22.1.1 Recurrent Events Data
522(1)
22.1.2 A Nonparametric Model for Recurrent Events Data
523(1)
22.2 Nonparametric Estimation of the MCF
524(5)
22.2.1 Nonparametric Model Assumptions
524(1)
22.2.2 Point Estimate of the MCF
525(1)
22.2.3 Confidence Intervals for Λ
525(4)
22.3 Comparison of two Samples of Recurrent Events Data
529(1)
22.4 Recurrent Events Data with Multiple Event Types
530(7)
Bibliographic Notes and Related Topics
533(1)
Exercises
534(3)
23 Case Studies and Further Applications
537(22)
23.1 Analysis of Hard Drive Field Data
537(3)
23.1.1 Data and Background
537(2)
23.1.2 The GLFP Model
539(1)
23.1.3 GLFP Likelihood for the Backblaze-14 Data
539(1)
23.1.4 Bayesian Estimation of the Backblaze-14 GLFP Model Parameters
539(1)
23.2 Reliability in the Presence of Stress--Strength Interference
540(5)
23.2.1 Definition of Stress--Strength Reliability
540(1)
23.2.2 Distributions of Stress and Strength
541(2)
23.2.3 ML Estimates and Confidence Intervals for Stress and Strength Reliability
543(1)
23.2.4 Bayesian Estimation for Stress and Strength Reliability
544(1)
23.3 Predicting Field Failures with a Limited Failure Population
545(8)
23.3.1 ML Analysis of the Device-J Field Data
545(3)
23.3.2 Bayesian Prediction for the Number of Future Device-J Failures
548(5)
23.4 Analysis of Accelerated Life-Test Data When There is a Batch Effect
553(6)
23.4.1 Kevlar Pressure Vessels Background and Data
553(1)
23.4.2 Model for the Kevlar Pressure Vessels ALT Data
553(1)
23.4.3 Bayesian Estimation and Reliability Inferences
554(2)
23.4.4 Bayesian Estimation of System Reliability
556(2)
Bibliographic Notes and Related Topics
558(1)
Epilogue
559(63)
A Notation and Acronyms
565(7)
B Other Useful Distributions and Probability Distribution Computations
572(16)
Introduction
572(1)
B.1 Important Characteristics of Distribution Functions
572(1)
B.1.1 Density and Probability Mass Functions
573(1)
B.1.2 Cumulative Distribution Function
573(1)
B.1.3 Quantile Function
573(1)
B.2 Distributions and R Computations
574(1)
B.3 Continuous Distributions
575(1)
B.3.1 Common Location-Scale and Log-Location-Scale Distributions
575(3)
B.3.2 Beta Distribution
578(1)
B.3.3 Uniform Distribution
579(1)
B.3.4 Loguniform Distribution
579(1)
B.3.5 Gamma Distribution
579(1)
B.3.6 Chi-Square Distribution
580(1)
B.3.7 Truncated Normal Distribution
580(1)
B.3.8 Student's t-Distribution
581(1)
B.3.9 Location-Scale t-Distribution
582(1)
B.3.10 Half Location-Scale t-Distribution
582(1)
B.3.11 Bivariate Normal Distribution
583(1)
B.3.12 Dirichlet Distribution
584(1)
B.4 Discrete Distributions
585(1)
B.4.1 Binomial Distribution
585(1)
B.4.2 Poisson Distribution
586(1)
B.4.3 Poisson-Binomial Distribution
587(1)
C Some Results from Statistical Theory
588(21)
Introduction
588(1)
C.1 The CDFS and PDFS of Functions of Random Variables
588(1)
C.1.1 Transformation of Continuous Random Variables
589(5)
C.2 Statistical Error Propagation---The Delta Method
594(2)
C.3 Likelihood and Fisher Information Matrices
596(1)
C.4 Regularity Conditions
596(1)
C.4.1 Regularity Conditions for Location-Scale Distributions
597(1)
C.4.2 General Regularity Conditions
597(1)
C.4.3 Asymptotic Theory for Nonregular Models
598(1)
C.5 Convergence in Distribution
598(1)
C.5.1 Central Limit Theorem and Other Examples of Convergence in Distribution
599(1)
C.6 Convergence in Probability
600(1)
C.7 Outline of General ML Theory
601(1)
C.7.1 Asymptotic Distribution of ML Estimators
601(1)
C.7.2 Asymptotic Variance--Covariance Matrix for Test Planning
601(1)
C.7.3 Asymptotic Distribution of Functions of ML Estimators
601(1)
C.7.4 Estimating the Variance--Covariance Matrix of ML Estimates
602(1)
C.7.5 Likelihood Ratios and Profile Likelihoods
602(1)
C.7.6 Approximate Likelihood-Ratio-Based Confidence Regions or Confidence Intervals for the Model Parameters
603(1)
C.7.7 Approximate Confidence Regions and Intervals Based on Asymptotic Normality of ML Estimators
603(1)
C.8 Inference with Zero or Few Failures
604(1)
C.8.1 Exponential Distribution Inference with Zero or Few Failures
604(2)
C.8.2 Weibull Distribution Inference with Given β and Zero or Few Failures
606(1)
C.9 The Bonferroni Inequality
607(2)
D Tables
609(13)
References 622(25)
Index 647
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.