Reliability analysis for shock systems based on damage evolutions via Markov processes
研究了冲击到达后损伤随时间演化（如自愈、恶化）的两种冲击模型，推导了系统可靠性及损伤消失或导致系统失效的概率，并给出了三种到达间隔分布下的数值例子。
Abstract Reliability evaluation under shock models has attracted considerable attention in the literature. Existing research on shock models has focused primarily on damage effects of shocks treated as constants after the arrivals of shocks. Due to the presence of self‐healing, deterioration, and variation over time, the damage effects caused by the shocks may have some evolutions. In this work, we focus on arrivals of shocks that follow a continuous‐time renewal process, and a Markov process that describes the evolution of shock damage. In this regard, we develop here two kinds of shock models and then derive system reliabilities under these two kinds of shock models. The asymptotic behavior of the damage evolution process of each shock is then discussed, and the probabilities of each shock eventually disappearing and destroying the system are derived through the use of aggregated stochastic processes. Finally, the results and numerical examples are presented for three special cases, namely: (1) when the inter‐arrival times of the shocks follow exponential distribution, (2) when the inter‐arrival times of the shocks follow Erlang distribution, and (3) when the inter‐arrival times of the shocks follow uniform distribution.