Robust Degradation Analysis With Non-Gaussian Measurement Errors

Abstract

Degradation analysis is an effective way to infer the health status and lifetime of products. Due to variability in the measurement, degradation observations are often subject to measurement errors. Existing studies generally assume Gaussian measurement errors, which may be deficient when there are outliers in the observations. To make a robust inference, we propose a Wiener degradation model with measurement errors modeled by Student's t-distribution. The t-distribution is a useful extension to the Gaussian distribution that provides a parametric approach to robust statistics. Nevertheless, the resulting likelihood function involves multiple integrals, which makes direct maximization difficult. Therefore, we propose an expectation-maximization algorithm, where the variational Bayes technique is introduced to derive an approximate conditional distribution in the E-step. The effectiveness of the proposed model is validated through Monte Carlo simulations. The applicability of the robust method is illustrated through applications to the degradation data of lithium-ion batteries and hard disk drives.