Approximate Tolerance Limits Under Log-Location-Scale Regression Models in the Presence of Censoring

Abstract

For a product manufactured in large quantities, tolerance limits play a fundamental role in setting limits on the process capability. Existing methodologies for setting tolerance limits in life test experiments focus primarily on one-sample problems. In this study, we extend tolerance limits in the presence of covariates in life test experiments. A method constructing approximate tolerance limits is proposed under log-location-scale regression models, a class of models used widely in reliability and life test experiments. The method is based on an application of the large sample theory of maximum likelihood estimators, which is modified by a bias-adjustment technique to enhance small sample accuracy. The proposed approximate tolerance limits are shown asymptotically to have nominal coverage probability under the assumption of "independent censoring." This includes Type I and Type II censoring schemes. Simulation studies are conducted to assess finite sample properties under the log-location-scale regression models. The method is illustrated with two datasets. R codes for implementing the proposed method are available online on the Technometrics web site, as supplemental materials.