Optimal Stress Levels in Accelerated Degradation Testing for Various Degradation Models

TL;DR

This paper develops optimal experimental designs for accelerated degradation testing using gamma process models, improving lifetime estimation accuracy for reliable products under various stress conditions.

Contribution

It introduces an algorithm-based optimal design framework for univariate and bivariate gamma process degradation models, including mixed effects models, for accelerated testing.

Findings

Optimal designs minimize variance in failure time estimates.

Sensitivity analysis shows robustness of designs under parameter misspecification.

Extension to bivariate models enhances applicability for complex degradation processes.

Abstract

Accelerated degradation tests are used to provide accurate estimation of lifetime characteristics of highly reliable products within a relatively short testing time. Data from particular tests at high levels of stress (e.g., temperature, voltage, or vibration) are extrapolated, through a physically meaningful statistical model, to attain estimates of lifetime quantiles at normal use conditions. The gamma process is a natural model for estimating the degradation increments over certain degradation paths, which exhibit a monotone and strictly increasing degradation pattern. In this work, we derive first an algorithm-based optimal design for a repeated measures degradation test with single failure mode that corresponds to a single response component. The univariate degradation process is expressed using a gamma model where a generalized linear model is introduced to facilitate the derivation of an optimal design. Consequently, we extend the univariate model and characterize optimal designs for accelerated degradation tests with bivariate degradation processes. The first bivariate model includes two gamma processes as marginal degradation models. The second bivariate models is expressed by a gamma process along with a mixed effects linear model. We derive optimal designs for minimizing the asymptotic variance for estimating some quantile of the failure time distribution at the normal use conditions. Sensitivity analysis is conducted to study the behavior of the resulting optimal designs under misspecifications of adopted nominal values.