Shocks models with damage effect evolutions following Markov processes

Shock models have been widely studied in reliability area, because many real phenomena in reliability engineering can be depicted by the shock models. In general, the damage effects of shocks are treated as constants after the shocks arrive. In fact, the damage effects resulted from shocks may have some evolutions due to some self-healings, deteriorations and variations over time. In the present paper, three types of shock models with damage effect evolutions following Markov processes are developed in discrete time situations, then the system reliability formulas and the means and variances of their lifetimes are given. The relationship among the introduced shock models is discussed, and some special cases for three types of shock models are also studied. The asymptotic behaviors of damage evolution processes are presented for a special case. Some numerical examples are presented to illustrate the results obtained in the paper.