Bayesian Life Test Planning for Log-Location-Scale Family of Distributions

Abstract

This paper describes Bayesian methods for life test planning with censored data from a log-location-scale distribution when prior information of the distribution parameters is available. We use a Bayesian criterion based on the estimation precision of a distribution quantile. A large-sample normal approximation gives a simplified, easy-to-interpret, yet valid approach to this planning problem, where in general no closed-form solutions are available. To illustrate this approach, we present numerical investigations using the Weibull distribution with type II censoring. We also assess the effects of prior distribution choice. A simulation approach of the same Bayesian problem is also presented as a tool for visualization and validation. The validation results generally are consistent with those from the large-sample approximation approach.