Two-Stage Maximum Likelihood Estimation Procedure for Parallel Constant-Stress Accelerated Degradation Tests

The parallel constant-stress accelerated degradation test (PCSADT) is a popular method used to assess the reliability of highly reliable products in a timely manner. Although the maximum likelihood (ML) method is commonly utilized to estimate the PCSADT parameters, the explicit forms of the ML estimators, and their corresponding Fisher information matrix are usually difficult to obtain. In this article, we propose a two-stage ML (TSML) estimation procedure for a time-transformed model. In the proposed procedure, all the TSML estimators not only have explicit expressions but also possess consistency and asymptotic normality. Hence, this method is tractable for reliability engineers. Furthermore, the TSML estimators can provide constructive information about the unknown accelerated relationship law. The proposed method is also applied to analyze light-emitting diode data and compare the performance of our estimation procedures with the ML method via simulations.