Designing Bayesian Reliability Sampling Plans for Weibull Lifetime Models Using Progressively Censored Data

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Mathematics & Actuarial Science Department

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Maram Salem; Zeinab Amin; Moshira Ismail

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Research Article

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International Journal of Reliability, Quality and Safety Engineering

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This paper presents Bayesian reliability sampling plans for the Weibull distribution based on progressively Type-II censored data with binomial removals. In constructing sampling plans, the decision theoretic approach is used. A dependent bivariate nonconjugate prior is employed. The total cost of the sampling plan consists of sampling, time-consuming, rejection, and acceptance costs. The decision rule is based on the Bayes estimator of the survival function. Lindley's approximation is used to obtain Bayes estimates of the survival function under the quadratic and LINEX loss functions. However, the poor performance of Lindley's approximation with small sample sizes can be observed. The Metropolis-within-Gibbs Markov Chain Monte Carlo (MCMC) algorithm show significantly improved performance compared to Lindley's approximation. We use simulation studies to evaluate the Bayes risk and determine the optimal sampling plans for different sample sizes, observed number of failures, binomial removal probabilities and minimum acceptable reliability.

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