Classical and Bayes methods for Two-Sample prediction of a Weibull distribution

Two-Sample prediction is useful to develop scientific maintenance strategies, but its application is restricted due to the computation complexity. In this paper, lifetime prediction method is studied through constructing predictor and prediction limits for the minimum or, more generally, the jth smallest of a set of future observations from a Weibull population. For the sake of computation simplification, Newtonian binomial law is integrated into the modeling process, and explicit formulae for Weibull future order statistics are developed by classical Two-Sample prediction method only using current failure observations, and by Bayes Two-Sample prediction method using both previous and current failure data under Gamma prior distribution. A case study is presented, which illustrates methods to predict mud pump life. The predictor and one-sided lower prediction limits with different confidence level 0.80, 0.85, 0.90, 0.95 are given.