Reliability analysis for degraded systems in discrete time and discrete health states with stepwise failure threshold line

The degradation systems have attracted much attention in the past two decades, and most related works focus on continuous time and continuous health states, but the discrete time and discrete health states have not received widespread attention. In this paper, the reliability for discrete-time and discrete-health-status systems under two models has been considered in which the system goes through an irreversible degradation process with a non-increasing stepwise threshold. First, two system reliability models are developed by considering the discrete degradation processes with and without preventive maintenance (for short, PM). Then, two Markov chains are established: one is a conventional Markov chain, and another is a Markov chain containing momentary downward jumps for representing the PM. Finally, the block (recursive) operation is employed to alleviate the curse of dimensionality in the transition probability matrix for computations. Two application examples are presented to illustrate the computational procedures of reliability and its characteristics. All these findings can not only enrich the reliability models but also help the practitioners to use them to fit different scenarios on reliability evaluation, analysis and approximation. We believe the contents can shed light on discrete-time and discrete-state degradation models and analyses.