Bayesian step stress accelerated degradation testing design: A multi-objective Pareto-optimal approach

Abstract

Step-stress accelerated degradation testing (SSADT) aims to access the reliability of products in a short time. Bayesian optimal design provides an effective alternative to capture parameters uncertainty, which has been widely employed in SSADT design by optimizing specified utility objective. However, there exist several utility objectives in Bayesian SSADT design; for the engineers, it causes much difficulty to choose the right utility specification with the budget consideration. In this study the problem is formulated as a multi-objective model motivated by the concept of Pareto optimization, which involves three objectives of maximizing the Kullback-Leibler (KL) divergence, minimizing the quadratic loss function of p-quantile lifetime at usage condition, and minimizing the test cost, simultaneously, in which the product degradation path is described by an inverse Gaussian (IG) process. The formulated programming is solved by NSGA-II to generate the Pareto of optimal solutions, which are further optimally reduced to gain a pruned Pareto set by data envelopment analysis (DEA) for engineering practice. The effectiveness of the proposed methodologies and solution method are experimentally illustrated by electrical connector's SSADT.