Maintenance Policy Of Repairable System With Delay Repair

The maintenance policy of the repairable system is an essential aspect in the researchof reliability, the maintenance model considering delay repair is a new topic in themaintenance policy. The one-component repairable system, the cold standby system, theseries system and the shock model are four important repairable systems. On the base ofthe references, the paper has generalized the four repairable systems, by using the renewalprocess, the geometric process and the α-power process, the objective functions underdifferent policies are deduced, the optimal policies of the systems are obtained, and theexistence of the optimal policies are checked.Firstly, the one-component repairable system with delay repair has studied. Thesystem has two types of failures when it breaks down. One is repairable, and the other canonly be removed by replacement. The replacement policy based on the failure number isconsidered. By using the renewal process and the α-power process, the explicit expressionof the long-run average cost per unit time is derived. Finally, we calculate the optimalpolicy by the numerical example, and the average cost is minimal.Secondly, the maintenance policy of the cold standby repairable system with delayrepair is studied. The replacement policy is considered respectively based on the failurenumber N and work life T for the component1, by using the geometric process and theα-power process, the explicit expression of the long-run expected downtime for repairequipment per unit time is derived. We prove that the existence of the optimal policy is tomake the long-run expected downtime for repair equipment per unit time the longest.Finally, the existence of optimal policy is demonstrated by the numerical example.Thirdly, the maintenance policy for the series system which consists of k dissimilarcomponents is studied. The replacement policy is considered based on the failure numbers,by using the renewal process and the geometric process, the system long-run average costper unit time is evaluated. Finally, an optimal policy is determined numerically.Finally, the maintenance policy for the shock model with one replaceable facility anddelay repair is studied. By using the geometric process and renewal process, a replacement policy is adopted by the failure numbers of the system, and the system long-run averagecost per unit time is evaluated. Finally, the optimal policy is obtained by the numericalexample.