The Maintenance Model Of System Based On Generalized Geometric Process

The normal operation of the system is the basis for maintaining the normal operation of life and the development of the industry.This paper studies the maintenance strategy of the sys-tem and establishes the maintenance model of single-component system and two-component cold standby system.Based on the cost-effectiveness ratio of long-term operation of the sys-tem,the optimal maintenance strategy of the system is given.The research content is divided into three parts:Study a simple system with only one component.It is assumed that two types of failures will occur during the operation of the system,a repairable type I failure and a non-repairable type II failure.When a type I failure occurs,perform a failure repair on the system immediately;when a type II failure occurs,replace the system.In the n-th cycle of the system opera-tion,when the continuous operation time of the system reaches?^n-1T,preventive repair is performed on it.Replace the system when either of the N-th type I failure and the first type II failure occurs first.The process of randomly decreasing continuous working time and randomly increasing continuous repairing time of the system is modeled by the gen-eralized geometric process,and a maintenance model is established with bivariate strategy(N,T).The expected cost per unit time of long-term operation of the system C(N,T)is given.Study a cold standby system with two identical components that with delayed repairs.The two components are exactly the same.Two components obey the principle of“failure first,repair first,and then wait for repair;one is in working state,and the other is cold standby”,when repairing and using.It is assumed that the failures occur during the operation of the system are all repairable failures.After the failure of the system,it may not be repaired in time because of the repairman may be on vacation or the missing parts required for repair.When the N-th failure occurs in component 2,replace the system.The system runs for a long time and gradually degenerates after repeated maintenance.The process of randomly reducing continuous working time of the system and randomly increasing continuous repair time is modeled by a generalized geometric process.The maintenance model is established with the univariate strategy N,and the average cost rate of the system for long-term opera-tion A(N)is given.Study a cold standby system with two different components with delayed repairs.The two components include the main component(component 1)and the spare component(compo-nent 2).Component 1 always takes priority over component 2 for repairing and using.The system gradually degenerates as the increasing number of failures.The process of randomly decreasing continuous working time and randomly increasing continuous repairing time of the system is modeled by the generalized geometric process.When the N-th failure of component 2 occurs,the system is replaced.The cost function of the system after long-term operation A(N)is given.Finally,assume that the life of the system obeys an exponential distribution.Solve the main-tenance models of the three systems by alternating search algorithm and search algorithm respectively,and get the optimal maintenance strategy.Numerical example results verify the rationality and practicability of the three models...