The Maintenance Replacement Policy Of Cold Standby System

The maintenance policy of the repairable system is an essential research in the reliability mathematics theory. In the model of maintenance policy, cold standby repairable system model is a very important model. On the base of the references, by using the geometric process and renewal process theorem, cold standby repairable system is analyzed in different conditions Dimensions and optimal policies of the systems are obtained.Firstly, under the condition of considering the discount rate and the rate of inflation and the fault unit cannot repair as new, two kinds of maintenance policies are researched based on the system of equipment life T and failure number N for the component 1. The explicit expressions of the long run total expected discounted benefits are derived. In some conditions, under the policy T we can prove that the existence and uniqueness of the optimal T is to make the long run total expected discounted benefits biggest. Using stochastic simulation methods, under the policy N the existence of optimal policy is demonstrated by the numerical example.Secondly, under the condition of considering the preventive maintenance and priority, the failure number N and the preventive maintenance interval T for the component 1 are used as policy. We establish an optimization model which regards the vacation time as objective function subjecting to the cost rate and the downtime. Under the known life distribution function of component 1, we prove that the long run average vacation time for repairman is monotonically increasing with T. The existence of optimal policy (T*,N*) is demonstrated by the numerical example.Thirdly, assume a repairman can take a single vacation and component 1 is given priority in use. A repair replacement policy N under which the system is replaced when the number of failures of the component 1 reaches N is also studied. The explicit expressions for the long-run average cost and downtime per unit time of the system are derived, and the corresponding optimal replacement policy N* can be found numerically. We provide a numerical example using stochastic simulation method to illustrate the theoretical results.Finally, on the basis of the previous chapter, we research component 1 has priority in use and repair and two parts cannot be repaired as good as new. A policy N is adopted by the Nth failure of the component 1. Under consideration of a repairman can take a single vacation or not, the explicit expressions for the long-run average cost per unit time of the system are derived respectively. We verify the existence and uniqueness of optimal policy N* and compare the results obtained in two cases.