The Replacement Policy Of Repairable System Based On Different Types Of Geometric Process

The replacement policy of the repairable system is an essential topic in the reliability mathematical theory. The replacement policy of the repairable system based on different types of geometric process has a certain practical significance. On the base of the references, the replacement policies of one unit and cold standby repairable systems are mainly studied by using traditional geometric process, the delayed geometric process and extended geometric process in this paper.Firstly, on the base of traditional geometric process, the replacement policy for a three-state repairable system with multiple delay vacations is studied. The system has two kinds of failure states, the first failure state is open circuit failure, which does not affect the life of the system, the second failure state is hardware failure and it can not be “as good as new”. The replacement policy is considered based on the total failure number of the system. The expressions of the average cost rate and the average repair rate are derived and the corresponding mathematical model is established. Finally, through a numerical example illustrates the existence of the results.Secondly, on the base of delayed geometric process, the replacement model of repairable system with selective multiple vacations is studied. At the beginning of each cycle, the repairman can select the vacation according to the actual situation. The replacement policy is considered based on the failure number of the system. The long-run expected cost per unit time is the objective function of the system, and the existence of the optimal replacement policy is proved. Finally, the feasibility of the method is verified by a numerical example.Finally, on the base of extended geometric process, the maintenance policy for a delayed repair cold standby repairable system with priority in use is studied. This system is consisting with two type components. The working life and repair time of the main component obeys the extended geometric process, and the standby component after failure can be “as good as new”. The repairman has a fault diagnosis time before repairing the faulty components. The replacement policy is considered based on the failure number of the main component. The expressions for the average cost rate and the average availability of the system are obtained. Finally, numerical simulation is used to verify the existence of the optimal replacement policy so that the average cost rate is lowest and the corresponding average availability is obtained.