Optimal Time Plan in Accelerated Degradation Testing

TL;DR

This paper develops a $c$-optimality criterion for designing accelerated degradation tests focusing on optimal timing, using linear mixed effects models, and evaluates robustness through numerical examples and sensitivity analysis.

Contribution

It introduces a novel $c$-optimality approach for time-based design in accelerated degradation testing, emphasizing timing over stress variable optimization.

Findings

Proposes a new $c$-optimality criterion for time design.

Demonstrates the approach with numerical examples.

Analyzes robustness of designs against parameter misspecification.

Abstract

Many highly reliable products are designed to function for years without failure. For such systems accelerated degradation testing may provide significance information about the reliability properties of the system. In this paper, we propose the $c$-optimality criterion for obtaining optimal designs of constant-stress accelerated degradation tests where the degradation path follow a linear mixed effects model. The present work is mainly concerned with developing optimal desings in terms of the time variable rather than considering an optimal design of the stress variable which is usually considered in the majority of the literature. Finally, numerical examples are presented and sensitivity analysis procedures are conducted for evaluating the robustness of the optimal as well as standard designs against misspecifications of the nominal values.