A gamma process based model for systems subject to multiple dependent competing failure processes under Markovian environments

The performance rules of many products that suffer from both natural degradation and random shocks may have discrepancies in different environments during their service life. This article proposes a reliability model for systems subject to multiple dependent competing failure processes affected by Markovian environments. The effect of dynamic environment is embodied in that the natural wear behavior of the system in different environments is controlled by distinct gamma processes. A maintenance model is developed in the case where switches of environment states take place only when systems are operating. Explicit formulas for system reliability indexes including the reliability function, first failure time distribution, mean time to first failure, and system availability are analytically derived in the form of Laplace transforms. In order to verify the correctness of the analytical formula, a simulation algorithm for evaluating the reliability function is proposed. Finally, they are applied to a study case of the micro-engine system, which illustrates the applicability of proposed models and the validity of obtained results.

Automated summary

The article proposes a reliability model for systems subject to multiple dependent competing failure processes affected by Markovian environments, with a maintenance model developed for distinct gamma processes controlling the natural wear behavior of the system in different environments. Analytically derived explicit formulas for system reliability indexes and a simulation algorithm are used to verify the correctness of the models and results. The applicability of the proposed models and the validity of obtained results are illustrated through a study case of a micro-engine system.