Generalized control-limit preventive repair policies for deteriorating cold and warm standby Markovian systems
研究了一个由N个独立同分布单元组成的可修退化马尔可夫系统，在冷备和温备模式下，通过动态规划证明了广义控制限策略在期望总折扣成本准则下的最优性，并给出了数值例子。
Consider a deteriorating repairable Markovian system with N stochastically independent identical units. The lifetime of each unit follows a discrete phase-type distribution. There is one online unit and the others are in standby status. In addition, there is a single repair facility and the repair time of a failed unit has a geometric distribution. The system is inspected at equally spaced points in time. After each inspection, either repair or a full replacement is possible. We consider state-dependent operating costs, repair costs that are dependent on the extent of the repair, and failure penalty costs. Applying dynamic programming, we show that under reasonable conditions on the system’s law of evolution and on the state-dependent costs, a generalized control-limit policy is optimal for the expected total discounted criterion for both cold standby and warm standby systems. Illustrative numerical examples are presented and insights are provided.