Shortest bayes credibility intervals for the lognormal failure model

Abstract

The lognormal distribution with density function f(x|λ,δ 2)= (2π) 1 2 δx −1 exp − ( In x−λ) 2 2δ 2 , forx>0,δ>0,−∞<λ<∞) is considered as a failure model from the Bayesian point of view. The shortest Bayesian confidence intervals for the parameters and reliability function are obtained for two cases. First, it is assumed that σ 2 is known and that γ has a normal prior distribution. Then, the case that γ is known and σ 2 has an inverted gamma prior distribution is considered. Some computer simulations are given to demonstrate the advantage of the shortest Bayesian confidence intervals over the ordinary Bayesian confidence intervals in terms of their length ratios.