A novel pseudo-maximum likelihood estimation method for accelerated degradation tests under Wiener process

For reliability assessment based on accelerated degradation tests (ADTs), an appropriate parameter estimation method is very important because it affects the extrapolation and prediction accuracy. The well-adopted maximum likelihood estimation (MLE) method focuses on interpolation fitting and obtains results via maximizing the likelihood of the observations. However, a best interpolation fitting does not necessarily yield a best extrapolation. In this paper, therefore, a pseudo-MLE (P-MLE) method is proposed to improve the prediction accuracy of constant-stress ADTs by considering the degradation mechanism equivalence under Wiener process. In particular, the degradation mechanism equivalence is characterized by a mechanism equivalence factor which presents the proportional relationship between degradation rate and variation. Then, the mechanism equivalence factor is determined via a two-step method. The other model parameters can be estimated by the general MLE method. The asymptotic variances of acceleration factors and the p-quantile of product failure time under normal condition are adopted to compare the statistical properties of the proposed method and the general MLE approach. Numerical examples show that the novel P-MLE method may not achieve a maximum likelihood but can provide more benefits regarding prediction accuracy enhancement especially when the sample size is limited.