Optimal Accelerated Degradation Testing Based on Bivariate Gamma Process with Dependent Components

TL;DR

This paper develops optimal experimental designs for accelerated degradation testing of systems with two components, considering both independent and dependent degradation paths modeled by a bivariate Gamma process with copula dependence.

Contribution

It introduces a framework for optimal ADT design using Gamma processes and copulas, addressing dependence between components and deriving D- and c-optimal designs.

Findings

Optimal designs minimize variance of lifetime quantile estimates.

D- and c-optimal designs are derived for dependent components.

Framework accommodates both independent and dependent degradation paths.

Abstract

Accelerated degradation testing (ADT) is one of the major approaches in reliability engineering which allows accurate estimation of reliability characteristics of highly reliable systems within a relatively short time. The testing data are extrapolated through a physically reasonable statistical model to obtain estimates of lifetime quantiles at normal use conditions. The Gamma process is a natural model for degradation, which exhibits a monotone and strictly increasing degradation path. In this work, optimal experimental designs are derived for ADT with two response components. We consider the situations of independent as well as dependent marginal responses where the observational times are assumed to be fixed and known. The marginal degradation paths are assumed to follow a Gamma process where a copula function is utilized to express the dependence between both components. For the case of independent response components the optimal design minimizes the asymptotic variance of an estimated quantile of the failure time distribution at the normal use conditions. For the case of dependent response components the $D$-criterion is adopted to derive $D$-optimal designs. Further, $D$- and $c$-optimal designs are developed when the copula-based models are reduced to bivariate binary outcomes.