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# Department of Statistics

## STAT 761

761—Reliability and Life Testing. (3) (Prereq. or Coreq: STAT 703 or 713) The various probability models and theory of inference used in reliability and life testing, including classes of life distributions, maintenance and replacement models, parametric and nonparametric theory, censoring.

Usually Offered: Fall Semesters, Odd years

Purpose: To expose the student to the basic concepts of reliability models and statistical inference for various probability models and methods used in life testing and reliability assessment, including parametric and nonparametric models, graphical methods, and classical and Bayesian inference procedures.

Current Textbook: Reliability Modelling: A Statistical Approach, Linda C. Wolstenholme, Chapman & Hall/CRC, 1999. Supplementary notes are also typically handed out.

 Topics Covered Chapters Time Introduction and Definitions of Reliability 1 0.5 weeks Lifetime distributions - Representations and interpretations, continuous and discretelifetime models, system lifetimes, classes.Parametric Models - Exponential, Weibull, extreme value, gamma, lognormal, etc. 2 1 week Reliability of coherent systems - series, parallel, k-out-of-n, pivotal decomposition, minimum cutsand paths, reliability bounds, etc. 6 1.2 weeks Nonparametric Reliability Estimation - Censored data; the Kaplan-Meier - PL estimator. 3 1.3 weeks Parametric models and inference based on likelihood methods. 4, 9 1.4 weeks Repairable systems. 5 0.3 weeks Graphical methods - probability plotting with uncensored and censored data, PL estimatortotal time on test plots, quantile-quantile plots, Weibull plots. 3, handouts 0.8 weeks Other topics - Reliability demonstrations tests, Accelerated life tests, Stress-strength models. 9.3,9.8,9.11,10.3,7.5-7.8 0.9 weeks Bayesian methods - Review of prior and posterior distributions, loss functions, Bayes estimator of reliability, etc. 10.8 0.6 weeks

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