Optimal Stress Levels in Accelerated Degradation Testing for Various Degradation Models

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 contribute with analytical results in regards to optimal design for accelerated degradation testing with single failure mode that corresponds to single response component. The univariate degradation process is expressed using a gamma model where the concept of generalized linear model is introduced to facilitate the derivation of an optimal design. Subsequently, we extend the univariate model to characterize optimal designs for accelerated degradation tests under different bivariate degradation models. 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 for the marginal components. Design optimization is conducted with respect to the minimum asymptotic variance criterion for estimating some quantile of the failure time distribution. Sensitivity analysis is considered to study the behavior of the resulting optimal designs under misspecifications of parameter values.