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

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 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.

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

“…the coefficient vector cpβq does not depend on α. It should be noted that, under the assumption of independent components, the result can be readily extended to r ą 2 components and to any s-out-of-r system, see (Shat, 2021) for further details in this regard. Under the premise that the locally optimal designs ξ l are supported on the endpoints of the design region r0, 1s, i. e., they are of the form ξ l " ξ w l , where ξ w l denotes a design with weight w 1l " w l on x 1l " 0 and weight w 2l " 1 ´w1l on x 2l " 1, (Shat and Schwabe, 2019) stated that the marginal optimal weight w l can be determined analytically by Elfving's theorem Elfving (1952),…”