Accelerated Life Test Plans Robust to Misspecification of the Stress—Life Relationship

Abstract

This article discusses methodology for deriving the asymptotic distribution of maximum likelihood estimators of model parameters in accelerated life tests (ALTs) when the form of the stress–life relationship is misspecified. If the practitioner can describe possible departures from an assumed ALT model, often linear in the appropriately transformed accelerating variable, then the results here can be used to obtain ALT plans that provide protection against potential bias and loss in estimation efficiency. General results are derived for log location-scale distributions and time-censored data, whereas specific results are presented for the lognormal and Weibull distributions. In a practical ALT situation, the methodology is applied to derive robust test plans based on minimizing asymptotic bias, asymptotic variance, or asymptotic mean squared error. Test plans are evaluated in terms of bias, efficiency, extrapolation to use level, and expected number failing.