Step Stress Accelerated Life Testing Data Analysis for Repairable System Using Proportional Intensity Model

Accelerated Life Testing (ALT) is used to obtain timely failure data to estimate life or reliability of the products under normal or special conditions. In the real situations, most failures at the system level are due to the failing of one component. The failed system is then repaired after the failure is detected. Most life data analysis of ALT addresses only non-repairable systems; no adequate data analysis of ALT has been found for repairable systems. This paper provides a statistical analysis of censored data obtained from Step Stress Accelerated Life Testing (SSALT) on a repairable system. A single accelerating variable with three stress levels is analyzed extensively. The stress change times in SSALT are fixed and the observed failure data are time-censored. In this paper, a "minimal repairing" approach for the repairable system is assumed. The Paw Law Process (PLP) is modeled to describe the reliability change process of the repairable system. Proportional Intensity (PI) regression model is then used to analyze failure data of the repairable system with covariates based on PLP. Based on cumulative intensity functions under different stress levels, a SSALT model for the repairable system is developed. Maximum Likelihood Estimates (MLE) and the log-likelihood function are derived, and a maximizing procedure is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation studies.