Progressively Censored Reliability Sampling Plans Based on Mean Product Lifetime

Abstract

Reliability sampling plans are often used to determine the compliance of the product with relevant quality standards and customers’ expectations and needs. This paper presents a proposed design of reliability sampling plans when the underlying lifetime model is Weibull based on progressively Type-II censored data in the presence of binomial removals. We employ Bayesian decision theory using the Bayes estimator of the mean product lifetime. When both parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. The Bayes estimators of the mean lifetime are evaluated using the Metropolis-within-Gibbs algorithm, under the assumption of mean squared error loss as well as the linear-exponential (LINEX) loss commonly used in the literature on asymmetric loss. The corresponding probability density functions are estimated using kernel density estimation. A cost function which includes the sampling cost, the cost of the testing time, as well as acceptance and rejection costs is proposed to determine the Bayes risk and the corresponding optimal sampling plan. We illustrate, through simulation studies as well as a real life data set, the application of the proposed method. Sensitivity of the proposed plans is performed.

Appendix

Figure 3

Trace plots of a Markov Chain used for evaluating: (a) ${\widehat {\mu }}_{Q}$, (b) ${\widehat {\mu }}_{L}$ with k = 1.5, and (c) ${\widehat {\mu }}_{L}$ with k = 2.5

Figure 4

Autocorrelation plots of a Markov Chain used for evaluating: (a) ${\widehat {\mu }}_{Q}$, (b) ${\widehat {\mu }}_{L}$with k = 1.5, and (c) ${\widehat {\mu }}_{L}$ with k = 2.5