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This volume—dedicated to William Q. Meeker on the occasion of his sixtieth birthday—is a collection of invited chapters covering recent advances in accelerated life testing and degradation models. The book covers a wide range of applications to areas such as reliability, quality control, the health sciences, economics, and finance. Specific topics covered include: * Accelerated testing and inference * Step-stress testing and inference * Nonparametric inference * Model validity in accelerated testing * The point process approach * Bootstrap methods in degradation analysis * Exact inferential methods in reliability * Dynamic perturbed systems * Degradation models in statistics Advances in Degradation Modeling is an excellent reference for researchers and practitioners in applied probability and statistics, industrial statistics, the health sciences, quality control, economics, and finance.

Accelerated life testing --- Accelerated testing --- Life testing, Accelerated --- Reliability testing --- Statistical methods. --- Mathematics. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Testing --- Distribution (Probability theory. --- Mathematical statistics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics . --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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Stochastic processes --- Reliability (Engineering) --- Mathematical models

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Mathematical statistics --- Estimation theory. --- Point processes. --- Statistique mathématique --- Statistique mathématique --- Mathematical statistics. --- Estimation, Théorie de l' --- Statistique mathematique --- Analyse multivariee

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"If the number of sample observations n ! 1, the statistic in (1.1) will follow the chi-squared probability distribution with r-1 degrees of freedom. We know that this remarkable result is true only for a simple null hypothesis when a hypothetical distribution is specified uniquely (i.e., the parameter is considered to be known). Until 1934, Pearson believed that the limiting distribution of the statistic in (1.1) will be the same if the unknown parameters of the null hypothesis are replaced by their estimates based on a sample; see, for example, Baird (1983), Plackett (1983, p. 63), Lindley (1996), Rao (2002), and Stigler (2008, p. 266). In this regard, it is important to reproduce the words of Plackett (1983, p. 69) concerning E. S. Pearson's opinion: "I knew long ago that KP (meaning Karl Pearson) used the 'correct' degrees of freedom for (a) difference between two samples and (b) multiple contingency tables. But he could not see that in curve fitting should be got asymptotically into the same category." Plackett explained that this crucial mistake of Pearson arose from to Karl Pearson's assumption "that individual normality implies joint normality." Stigler (2008) noted that this error of Pearson "has left a positive and lasting negative impression upon the statistical world." Fisher (1924) clearly showed 1 2 CHAPTER 1. A HISTORICAL ACCOUNT that the number of degrees of freedom of Pearson's test must be reduced by the number of parameters estimated from the sample"--

Chi-square test. --- Distribution (Probability theory)

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An outgrowth of the sixth conference on “Mathematical Methods in Reliability: Theory, Methods, and Applications,” this book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by recognized experts in the field of reliability, the contributions cover a wide range of models, methods, and applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation. The volume is thematically organized into four major sections: * Reliability Models, Methods, and Optimization; * Statistical Methods in Reliability; * Applications; * Computer Tools for Reliability. Mathematical and Statistical Models and Methods in Reliability is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.

Statistical science --- Operational research. Game theory --- Probability theory --- Mathematics --- Biomathematics. Biometry. Biostatistics --- Hygiene. Public health. Protection --- Applied physical engineering --- Planning (firm) --- Plant and equipment --- Production management --- betrouwbaarheid --- medische statistiek --- toegepaste wiskunde --- waarschijnlijkheidstheorie --- stochastische analyse --- veiligheid (bouw) --- biostatistiek --- economie --- mathematische modellen --- statistiek --- wiskunde --- kwaliteitscontrole --- kansrekening --- statistisch onderzoek