A prediction interval approach to developing life test acceptance criteria for progressively censored data

Abstract

In this paper we use the prediction-interval approach to construct acceptance criteria to determine whether or not certain batches of products are acceptable. The procedure is intended to protect both producers and consumers against highly defective lots and demonstrate that a required quality level is met with certain probability. The prediction interval approach is particularly useful to employ when the lifetime of the product represents the quality characteristic of interest. On the basis of a progressively censored sample from the Weibull lifetime distribution, the problem of constructing acceptance criteria by predicting a future lifetime based on an independent past sample of lifetimes from the same distribution is addressed in a Bayesian setting with a dependent bivariate prior. The Metropolis-within-Gibbs Sampler algorithm is used to obtain a sequence of draws from the posterior predictive distribution of future observations. This sequence is used to derive the prediction intervals based on which the lot acceptance criteria are determined. An example using real data is illustrated.