Inverting Tolerance Bounds for Confidence on a Specified Proportion of a Population Meeting a Specification

摘要

We consider methods to obtain the confidence that a specified proportion of the population meets a specification. For example, how confident are we that 90% (0.90) of the population does not exceed an upper specification? We show how confidence can be obtained by inverting tolerance bounds. Also, a Bayesian approach can be used to obtain a posterior probability that a specified proportion of the population meets a specification. We consider the single normal population and simple linear regression and nonlinear regression models. We also compare the two methods via a simulation study.