The Replacement Policy Of Repairable System Based On Degenerative Process

The maintenance policy of the repairable system is an essential topic in the reliabilitymathematics,the one unit repairable system with a replaceable repair facility and delayedgeometric process is a significant aspect.On the base of the references,the paper hasgeneralized the four repairable system:the α-power process system,the cold standbysystem,the system with two failure pattern and the repairable system with a replaceablerepair facility,by using the renewal process,the geometric process,the α-power processand delayed geometric process,the objective functions under different policies aregiven,the optimal policies of the systems are obtained,and the existence of the optimalpolicies are checked.Firstly, on the base of multiple vacations and α-power process,the one unitrepairable system has been studied.Assume that any the component after repair is not "asgood as new",we considered the two variable optimal replacement policy based on thefailure number and the working age for the system by using renew process theory and α-power process theory,the explicit expression of the long-turn expected profit per unit timeis derived.Finally,we analyze the optimal policy through numerical example.Secondly, the repairable system consists of two identical components has beenstudied with single repairman vacation.Under replacement policy of the working time,weprove that the existence of the optimal is to make the expected profit optimal.And weanalyze that the existence of the optimal is to make the long-turn expected profit per unittime the largest.Finally,the validity of the conclusion is demonstrated by the numericalexample.Thirdly, a cold standby repairable system consisting of two type components hasbeen studied.Failure mode, there are two, one is repairable, but it is not a "like-new" andthe other one is not repairable, resulting in replacement system.The maintenance policy isconsidered based on the failure number for component1.By using the geometric processand renewal process, the explicit expressions of the long-turn expected profit per unit timeand the average downtime are derived. Finally,an optimal policy is demonstrated by the numerical example.Finally,the one unit repairable system with a replaceable repair facility based ondelayed geometric process is studied.The working times of the replaceable repair facilityafter repair will become shorter and shorter,Ultimately, the replaceable repair facility willnot be able to work any longer and be replaced by a new. By using the delayed geometricprocess and renewal process, the explicit expressions of the long-turn expected cost perunit time are derived. Finally, a numerical example is given to illustrate some theoreticalresults.