Experimental designs for accelerated degradation tests based on linear mixed effects models

Accelerated degradation testing has considerable significance in reliability inference due to its ability to provide accurate estimation of lifetime characteristics of highly reliable systems within a relatively short testing time period. The measured data from particular experiments at high stress conditions are extrapolated, through a technically reasonable statistical model, to obtain estimates of certain reliability properties under normal use levels. In this work, we consider repeated measures accelerated degradation tests with multiple stress variables, where the degradation path is assumed to follow a linear mixed effects model which is quite common in settings when repeated measures are made. As opposed to the vast majority of numerical derivations in the literature, we contribute in this work with analytical results in regards to optimal experimental designs for minimizing the asymptotic variance for estimating the median failure time under normal use conditions when the time points for measurements are fixed in advance.