Optimal Design of Stress Levels in Accelerated Degradation Testing for Multivariate Linear Degradation Models

TL;DR

This paper develops optimal experimental designs for accelerated degradation testing with multiple failure modes, using linear mixed effects models to improve reliability estimation accuracy under fixed observation times.

Contribution

It introduces a novel optimal design methodology for multivariate linear degradation models in accelerated testing, enhancing reliability quantile estimation.

Findings

Optimal designs reduce the variance of lifetime quantile estimators.

Numerical examples demonstrate robustness and efficiency gains over standard designs.

The approach effectively handles competing failure modes in degradation data.

Abstract

In recent years, more attention has been paid prominently to accelerated degradation testing in order to characterize accurate estimation of reliability properties for systems that are designed to work properly for years of even decades. %In this regard, degradation data from particular testing levels of the stress variable(s) are extrapolated with an appropriate statistical model to obtain estimates of lifetime quantiles at normal use levels. In this paper we propose optimal experimental designs for repeated measures accelerated degradation tests with competing failure modes that correspond to multiple response components. The observation time points are assumed to be fixed and known in advance. The marginal degradation paths are expressed using linear mixed effects models. The optimal design is obtained by minimizing the asymptotic variance of the estimator of some quantile of the failure time distribution at the normal use conditions. Numerical examples are introduced to ensure the robustness of the proposed optimal designs and compare their efficiency with standard experimental designs.