A Bayesian Optimal Design for Accelerated Degradation Testing Based on the Inverse Gaussian Process

Abstract

Accelerated degradation testing (ADT) is commonly used to obtain degradation data of products by exerting loads over usage conditions. Such data can be used for estimating component lifetime and reliability under usage conditions. The design of ADT entails to establish a model of the degradation process and define the test plan to satisfy given criteria under the constraint of limited test resources. Bayesian optimal design is a method of decision theory under uncertainty, which uses historical data and expert information to find the optimal test plan. Different expected utility functions can be selected as objectives. This paper presents a method for Bayesian optimal design of ADT, based on the inverse Gaussian process and considering three objectives for the optimization: relative entropy, quadratic loss function, and Bayesian D-optimality. The Markov chain Monte Carlo and the surface fitting methods are used to obtain the optimal plan. By sensitivity analysis and a proposed efficiency factor, the Bayesian D-optimality is identified as the most robust and appropriate objective for Bayesian optimization of ADT.

Keywords

• Accelerated degradation testing
• Bayesian optimal design
• inverse Gaussian process
• Markov chain Monte Carlo (MCMC)
• surface fitting