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<p>Statistical Methods for Reliability Data i</p> <p>Preface to the Second Edition iii</p> <p>Preface to First Edition viii</p> <p>Acknowledgments xii</p> <p><b>1 Reliability Concepts and an Introduction to Reliability Data 1</b></p> <p>1.1 Introduction 1</p> <p>1.2 Examples of Reliability Data 3</p> <p>1.3 General Models for Reliability Data 11</p> <p>1.4 Models for Time to Event Versus Models for Recurrences in a Sequence of Events 13</p> <p>1.5 Strategy for Data Collection, Modeling, and Analysis 15</p> <p><b>2 Models, Censoring, and Likelihood for Failure-Time Data 19</b></p> <p>2.1 Models for Continuous Failure-Time Processes 19</p> <p>2.2 Models for Discrete Data from a Continuous Process 25</p> <p>2.3 Censoring 27</p> <p>2.4 Likelihood 28</p> <p><b>3 Nonparametric Estimation for Failure-Time Data 37</b></p> <p>3.1 Estimation from Complete Data 38</p> <p>3.2 Estimation from Singly-Censored Interval Data 38</p> <p>3.3 Basic Ideas of Statistical Inference 40</p> <p>3.4 Confidence Intervals from Complete or Singly-Censored Data 41</p> <p>3.5 Estimation from Multiply-Censored Data 43</p> <p>3.6 Pointwise Confidence Intervals from Multiply-Censored Data 45</p> <p>3.7 Estimation from Multiply-Censored Data with Exact Failures 47</p> <p>3.8 Nonparametric Simultaneous Confidence Bands 49</p> <p>3.9 Arbitrary Censoring 52</p> <p><b>4 Some Parametric Distributions Used in Reliability Applications 60</b></p> <p>4.1 Introduction 61</p> <p>4.2 Quantities of Interest in Reliability Applications 61</p> <p>4.3 Location-Scale and Log-Location-Scale Distributions 62</p> <p>4.4 Exponential Distribution 63</p> <p>4.5 Normal Distribution 64</p> <p>4.6 Lognormal Distribution 65</p> <p>4.7 Smallest Extreme Value Distribution 67</p> <p>4.8 Weibull Distribution 68</p> <p>4.9 Largest Extreme Value Distribution 70</p> <p>4.10 Frechet Distribution 71</p> <p>4.11 Logistic Distribution 73</p> <p>4.12 Loglogistic Distribution 74</p> <p>4.13 Generalized Gamma Distribution 75</p> <p>4.14 Distributions with a Threshold Parameter 76</p> <p>4.15 Other Methods of Deriving Failure-Time Distributions 78</p> <p>4.16 Parameters and Parameterization 80</p> <p>4.17 Generating Pseudorandom Observations from a Specified Distribution 80</p> <p><b>5 System Reliability Concepts and Methods 87</b></p> <p>5.1 Non-Repairable System Reliability Metrics 88</p> <p>5.2 Series Systems 88</p> <p>5.3 Parallel Systems 91</p> <p>5.4 Series-Parallel Systems 93</p> <p>5.5 Other System Structures 94</p> <p>5.6 Multistate System Reliability Models 96</p> <p><b>6 Probability Plotting 102</b></p> <p>6.1 Introduction 103</p> <p>6.2 Linearizing Location-Scale-Based Distributions 103</p> <p>6.3 Graphical Goodness of Fit 105</p> <p>6.4 Probability Plotting Positions 106</p> <p>6.5 Notes on the Application of Probability Plotting 111</p> <p><b>7 Parametric Likelihood Fitting Concepts: Exponential Distribution 119</b></p> <p>7.1 Introduction 120</p> <p>7.2 Parametric Likelihood 122</p> <p>7.3 Likelihood Confidence Intervals for θ 123</p> <p>7.4 Wald (Normal-Approximation) Confidence Intervals for θ 125</p> <p>7.5 Confidence Intervals for Functions of θ 126</p> <p>7.6 Comparison of Confidence Interval Procedures 127</p> <p>7.7 Likelihood for Exact Failure Times 128</p> <p>7.8 Effect of Sample Size on Confidence Interval Width and the Likelihood Shape 130</p> <p>7.9 Exponential Distribution Inferences with No Failures 131</p> <p><b>8 Maximum Likelihood Estimation for Log-Location-Scale Distributions 138</b></p> <p>8.1 Likelihood Definition 139</p> <p>8.2 Likelihood Confidence Regions and Intervals 142</p> <p>8.3 Wald Confidence Intervals 146</p> <p>8.4 The ML Estimate May Not Go Through the Points 151</p> <p>8.5 Estimation with a Given Shape Parameter 152</p> <p><b>9 Parametric Bootstrap and Other Simulation-Based Confidence Interval Methods 164</b></p> <p>9.1 Introduction 165</p> <p>9.2 Methods for Generating Bootstrap Samples and Obtaining Bootstrap Estimates 165</p> <p>9.3 Bootstrap Confidence Interval Methods 171</p> <p>9.4 Bootstrap Confidence Intervals Based on Pivotal Quantities 176</p> <p>9.5 Confidence Intervals Based on Generalized Pivotal Quantities 181</p> <p><b>10 An Introduction to Bayesian Statistical Methods for Reliability 189</b></p> <p>10.1 Bayesian Inference: Overview 190</p> <p>10.2 Bayesian Inference: an Illustrative Example 194</p> <p>10.3 More About Prior Information and Specification of a Prior Distribution 202</p> <p>10.4 Implementing Bayesian Analyses Using MCMC Simulation 205</p> <p>10.5 Using Prior Information to Estimate the Service-Life Distribution of a Rocket Motor 210</p> <p><b>11 Special Parametric Models 219</b></p> <p>11.1 Extending ML Methods 219</p> <p>11.2 Fitting the Generalized Gamma Distribution 220</p> <p>11.3 Fitting the Birnbaum–Saunders Distribution 223</p> <p>11.4 The Limited Failure Population Model 225</p> <p>11.5 Truncated Data and Truncated Distributions 227</p> <p>11.6 Fitting Distributions that Have a Threshold Parameter 232</p> <p><b>12 Comparing Failure-Time Distributions 243</b></p> <p>12.1 Background and Motivation 243</p> <p>12.2 Nonparametric Comparisons 244</p> <p>12.3 Parametric Comparison of Two Groups by Fitting Separate Distributions 247</p> <p>12.4 Parametric Comparison of Two Groups by Fitting Separate Distributions With Equal σ values 248</p> <p>12.5 Parametric Comparison of More than Two Groups 250</p> <p><b>13 Planning Life Tests for Estimation 261</b></p> <p>13.1 Introduction 261</p> <p>13.2 Simple Formulas to Determine the Needed Sample Size 263</p> <p>13.3 Use of Simulation in Test Planning 267</p> <p>13.4 Approximate Variance of ML Estimators and Computing Variance Factors 274</p> <p>13.5 Variance Factors for (Log-)Location-Scale Distributions 275</p> <p>13.6 Some Extensions 278</p> <p><b>14 Planning Reliability Demonstration Tests 282</b></p> <p>14.1 Introduction to Demonstration Testing 282</p> <p>14.2 Finding the Required Sample Size n or Test-Length Factor k 284</p> <p>14.3 Probability of Successful Demonstration 288</p> <p><b>15 Prediction of Failure Times and the Number of Future Field Failures 293</b></p> <p>15.1 Basic Concepts of Statistical Prediction 294</p> <p>15.2 Probability Prediction Intervals (_ Known) 295</p> <p>15.3 Statistical Prediction Intervals (_ Estimated) 296</p> <p>15.4 Plug-In Prediction and Calibration 297</p> <p>15.5 Computing and Using Predictive Distributions 301</p> <p>15.6 Prediction of the Number of Future Failures from a Single Group of Units in the Field 304</p> <p>15.7 Predicting the Number of Future Failures from Multiple Groups of Units in the Field with Staggered Entry into the Field 307</p> <p>15.8 Bayesian Prediction Methods 311</p> <p>15.9 Choosing a Distribution for Making Predictions 313</p> <p><b>16 Analysis of Data with More than One Failure Mode 321</b></p> <p>16.1 An Introduction to Multiple Failure Modes 321</p> <p>16.2 Model for Multiple Failure Modes Data 323</p> <p>16.3 Competing-Risk Estimation 324</p> <p>16.4 The Effect of Eliminating a Failure Mode 328</p> <p>16.5 Subdistribution Functions and Prediction for Individual Failure Modes 331</p> <p>16.6 More About the Non-Identifiability of Dependence Among Failure Modes 332</p> <p><b>17 Failure-Time Regression Analysis 340</b></p> <p>17.1 Introduction 341</p> <p>17.2 Simple Linear Regression Models 342</p> <p>17.3 Standard Errors and Confidence Intervals for Regression Models 345</p> <p>17.4 Regression Model with Quadratic μ and Nonconstant σ 347</p> <p>17.5 Checking Model Assumptions 351</p> <p>17.6 Empirical Regression Models and Sensitivity Analysis 354</p> <p>17.7 Models with Two or More Explanatory Variables 359</p> <p><b>18 Analysis of Accelerated Life Test Data 369</b></p> <p>18.1 Introduction to Accelerated Life Tests 369</p> <p>18.2 Overview of ALT Data Analysis Methods 371</p> <p>18.3 Temperature-Accelerated Life Tests 372</p> <p>18.4 Bayesian Analysis of a Temperature-Accelerated Life Test 380</p> <p>18.5 Voltage-Accelerated Life Test 381</p> <p><b>19 More Topics on Accelerated Life Testing 396</b></p> <p>19.1 ALTs with Interval-Censored Data 396</p> <p>19.2 ALTs with Two Accelerating Variables 401</p> <p>19.3 Multifactor Experiments with a Single Accelerating Variable 405</p> <p>19.4 Practical Suggestions for Drawing Conclusions from ALT Data 409</p> <p>19.5 Pitfalls of Accelerated Life Testing 410</p> <p>19.6 Other Kinds of Accelerated Tests 412</p> <p><b>20 Degradation Modeling and Destructive Degradation Data Analysis 421</b></p> <p>20.1 Degradation Reliability Data and Degradation Path Models: Introduction and Background422</p> <p>20.2 Description and Mechanistic Motivation for Degradation Path Models 423</p> <p>20.3 Models Relating Degradation and Failure 427</p> <p>20.4 DDT Background, Motivating Examples, and Estimation 427</p> <p>20.5 Failure-Time Distributions Induced from DDT Models and Failure-Time Inferences 431</p> <p>20.6 ADDT Model Building 433</p> <p>20.7 Fitting an Acceleration Model to ADDT Data 435</p> <p>20.8 ADDT Failure-Time Inferences 437</p> <p>20.9 ADDT Analysis Using an Informative Prior Distribution 438</p> <p>20.10 An ADDT with an Asymptotic Model 439</p> <p><b>21 Repeated-Measures Degradation Modeling and Analysis 448</b></p> <p>21.1 RMDT Models and Data 448</p> <p>21.2 RMDT Parameter Estimation 451</p> <p>21.3 The Relationship Between Degradation and Failure-Time for RMDT Models 454</p> <p>21.4 Estimation of a Failure-Time cdf from RMDT Data 457</p> <p>21.5 Models for ARMDT Data 458</p> <p>21.6 ARMDT Estimation 459</p> <p>21.7 ARMDT with Multiple Accelerating Variables 462</p> <p><b>22 Analysis of Repairable System and Other Recurrent Events Data 469</b></p> <p>22.1 Introduction 469</p> <p>22.2 Nonparametric Estimation of the MCF 471</p> <p>22.3 Comparison of Two Samples of Recurrent Events Data 474</p> <p>22.4 Recurrent Events Data with Multiple Event Types 475</p> <p><b>23 Case Studies and Further Applications 481</b></p> <p>23.1 Analysis of Hard Drive Field Data 481</p> <p>23.2 Reliability in the Presence of Stress-Strength Interference 484</p> <p>23.3 Predicting Field Failures with a Limited Failure Population 487</p> <p>23.4 Analysis of Accelerated Life Test Data When There is a Batch Effect 494</p> <p>Epilogue 499</p> <p><b>A Notation and Acronyms 503</b></p> <p><b>B Other Useful Distributions and Probability Distribution Computations 509</b></p> <p>B.1 Important Characteristics of Distribution Functions 509</p> <p>B.2 Distributions and R Computations 511</p> <p>B.3 Continuous Distributions 511</p> <p>B.4 Discrete Distributions 519</p> <p>B.4.1 Binomial Distribution 519</p> <p><b>C Some Results from Statistical Theory 522</b></p> <p>C.1 The cdfs and pdfs of Functions of Random Variables 522</p> <p>C.2 Statistical Error Propagation—The Delta Method 527</p> <p>C.3 Likelihood and Fisher Information Matrices 528</p> <p>C.4 Regularity Conditions 529</p> <p>C.5 Convergence in Distribution 530</p> <p>C.6 Convergence in Probability 531</p> <p>C.7 Outline of General ML Theory 532</p> <p>C.8 Inference with Zero or Few Failures 534</p> <p>C.9 The Bonferroni Inequality 536</p> <p><b>D Tables 538</b></p> <p>References 549</p>

<p><b> William Q. Meeker, PhD,</b> 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.</p> <p><b> Luis A. Escobar, PhD,</b> 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. <p><b> Francis G. Pascual, PhD,</b> is an Associate Professor in the Department of Mathematics and Statistics at Washington State University.

<p><b>An authoritative guide to the most recent advances in statistical methods for quantifying reliability</b></p> <p><i>Statistical Methods for Reliability Data, Second Edition</i> (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. <p>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. <p>SMRD2 features: <ul><li>Contains a wealth of information on modern methods and techniques for reliability data analysis</li> <li>Offers discussions on the practical problem-solving power of various Bayesian inference methods </li> <li>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 </li> <li>Includes helpful technical-problem and data-analysis exercise sets at the end of every chapter</li> <li>Presents illustrative computer graphics that highlight data, results of analyses, and technical concepts </li></ul> <p>Written for engineers and statisticians in industry and academia, <i>Statistical Methods for Reliability Data, Second Edition</i> offers an authoritative guide to this important topic.

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