Lognormal and Weibull accelerated life test plans under distribution misspecification

In this article, we derive expressions for the asymptotic distribution of maximum likelihood estimators of model parameters in accelerated life tests (ALTs) when the model distribution is misspecified. We investigate results for two popular models, namely, the lognormal and Weibull Arrhenius-type ALT models. We propose test plan criteria based on asymptotic bias (ABias) and asymptotic mean squared error (AMSE) to derive ALT test plans. We derive 4:2:1 allocation plans that minimize either ABias² or AMSE. These criteria provide control over estimation bias and variance when the model distribution is misspecified.