Tolerance Intervals for Variance Component Models Using Bayesian Simulation

Abstract

This article presents a simulation-based approach for determining Bayesian tolerance intervals in variance component models. The approach handles different kinds of tolerance intervals in a straightforward fashion and is easily tailored to particular applications. It utilizes a computer-generated sample from the joint posterior distribution of the mean and variance parameters to construct a sample from other relevant posterior distributions. An aircraft manufacturing example illustrates important features of the method, including the use of informative and noninformative priors and relationships with frequentist methodologies.