Approximate Tolerance Limits Under Log-location-scale Regression Models in Presence of Censoring

Abstract

For a product manufactured in large quantities, tolerance limits plays a fundamental role in setting limits on the process capability. Existing methodologies for tolerance limits on life test experiments are primarily focusing on the one-sample problem. In this talk, we present a method to extend tolerance limits in presence of covariates that characterizes heterogeneity in life test experiments. Methods of constructing approximate tolerance limits are proposed under log-location-scale regression models, a widely used class of models in reliability and life test experiments. The method utilizes a bias-adjustment technique to enhance small sample accuracy, which is motivated by the classical results for the optimal tolerance limit. Simulation studies are conducted to assess finite sample properties under selected members from the log-location-scale regression models, and to compare with existing methods. The method is illustrated with an application to the numbers of hours of motorettes operating under various temperatures.