Economic and economic‐statistical designs of an &Xmacr; control chart for two‐unit series systems with condition‐based maintenance

The economic and economic‐statistical designs of an &Xmacr; control chart for two‐identical unit series systems with condition‐based maintenance is studied in this paper. This system is described using a five‐state continuous time Markov chain. We assume that the system is monitored by an &Xmacr; control chart to avoid costly failures. When the control chart gives an out‐of‐control signal, a full inspection will be conducted to confirm the actual system condition. Moreover, we assume that the system unit can be preventively replaced at a sampling epoch and must be replaced upon failure; the cost of preventive replacement is less than that of failure replacement. In addition, a random shift size is considered for two types of design. Based on these assumptions and by using renewal theory, optimization models have been developed to find the optimal control chart parameters for minimizing the average maintenance costs. A numerical example is presented to compare the two control chart designs. We also consider the effect of each statistical constraint on the decision variables and on the expected cost.