Experimental Designs for Accelerated Degradation Tests Based on Linear Mixed Effects Models

TL;DR

This paper develops optimal experimental designs for accelerated degradation tests using linear mixed effects models, aiming to improve lifetime estimation accuracy under multiple stress variables.

Contribution

It introduces methods to optimize experimental designs for repeated measures degradation tests with multiple stress factors, focusing on minimizing variance in median failure time estimates.

Findings

Derived optimal designs for fixed measurement times.

Extended design optimization to variable measurement schedules.

Enhanced accuracy in lifetime quantile estimation.

Abstract

Accelerated degradation tests are used to provide accurate estimation of lifetime properties of highly reliable products within a relatively short testing time. There data from particular tests at high levels of stress (e.\,g.\ temperature, voltage, or vibration) are extrapolated, through a physically meaningful model, to obtain estimates of lifetime quantiles under normal use conditions. In this work, we consider repeated measures accelerated degradation tests with multiple stress variables, where the degradation paths are assumed to follow a linear mixed effects model which is quite common in settings when repeated measures are made. We derive 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 either fixed in advance or are also to be optimized.