Reliability Analysis of Repairable Systems With Incomplete Failure Time Data

Abstract

Reliability analysis of repairable systems has been widely conducted based on collected information such as the systems’ failure counting processes. In many real-life situations, the failure counting processes may not be completely observed when some failure times are not recorded or missing due to various practical reasons. In the literature, only a limited number of reliability studies focus on missing failure time data for repairable systems with an assumption that the system repair is either perfect or minimal. When the repair effect is general as in many real-world situations, challenges arise for reliability analysis in that the observed and unobserved failure times are statistically dependent in a complex manner, and the time censoring problem becomes unconventional. In this paper, to overcome these challenges, we propose a reliability model for repairable systems with incomplete failure time data under general repair. The proposed model is suitable for modeling both a single system and multiple systems subject to failure heterogeneity. A maximum likelihood estimation method is developed to estimate the model parameters. Based on the proposed model, statistical inference of the missing times is developed. Simulation and real-life case studies are conducted to verify the developed methods.