A Bayesian estimation procedure of reliability function for lifetime distributions

Abstract

This paper is a sequel to [1], wherein we proposed a simple procedure to construct the joint prior and posterior distributions of Weibull parameters based on the underlying reliability function estimates in two time cross-sections. In this paper, we extend the procedure in three aspects: a) the prior data can now be taken in terms of a simple probability paper plot, b) the posterior now includes not only posterior estimates of distribution parameters, but also the posterior estimate of the underlying reliability function along with the respective credibility intervals, and c) we show that the proposed procedures can be applied to any parametric lifetime distribution, not necessarily limited to the location-scale family.