Bayes shrinkage estimation of reliability and the parameters of a finite range failure time model

Abstract

A finite range failure time distribution has been proposed and studied. For estimating the two parameters of this distribution, this paper considers a prior assumption that (1 − b) is the probability that the scale parameter θ and shape parameter p have the values θ 0 and p 0, respectively, and that the rest of the probability mass b(0 ≤ b ≤ 1) is distributed as h( p, θ) = h 1( p) h 2( θ). The value h 1( p) is a uniform density for p and h 2( θ) is an inverted gamma density for θ. With this prior density, Bayes estimators are first obtained and then Bayesian shrinkage estimators are defined. Bayesian shrinkage estimators are compared with maximum likelihood estimators (m.l.e.) and it was found that the proposed estimators are better than m.l.e. for quite a wide range of parameters.