Research On The Optimal Maintenance And Replacement Policies Of The Multi-component And Multi-state Deteriorate System

In system maintenance problems,most systems assume that they can repair "as good as new" after a failure.In fact,during the operation of the system,due to the deterioration of the system,most systems are degraded.The successive working time after each repair are shorter and shorter,while the successive repair time after repair are longer and longer.So using a monotonous process to describe this degenerate system is more reasonable.In practice,a system does not have only one component,and each component may have multiple failure states.Geometric Process has a widely used in theoretical problem.According to the geometric process theory and the update process theory,several multi-component and multi-state degeneracy system models have been established in this paper.The average cost expression of the system over a long period of time has been derived,the existence of the optimal strategy for the model has been verified and the numerical results of the optimal replacement strategy are given.First,the optimal maintenance strategy of multi-state repairable series system based on geometric process is studied.Assume that the system has k components and each component has l +1 states,and the components cannot be repaired as good as new.Adopted maintenance policy based on the number of failures of each component in the system,and it is used as the replacement strategy and the objective function is the minimum average cost per unit of time for the long-term operation of the system.According to the geometric process theory and the update process theory,a reliability mathematical model is established.The existence of the optimal maintenance replacement strategy of the model is proved and this method is not limited by the specific expressions expected.The numerical examples are used to illustrate the validity of the model and the sensitivity analysis of the parameters are also given.Then,the optimal maintenance strategy for multi-state repairable series systems with preventive maintenance is studied.Assume that the system has k components and each com-ponent has l + 1 failure state.When the reliability of the system component is reduced to a fixed value,the system is maintained preventively.Adopted maintenance policy based on the number of failures of various components in the system as(R,N1,…,Nk),the average cost expression of the system for a long period of time is derived,and the optimal mainte-nance and replacement strategy of the system are presented numerically and the rationality of maintenance replacement model is verified.Finally,the optimal maintenance replacement strategy for multi-state cold-standby sys-tem with cold-storage components is studied.Assuming the system consists of two compo-nents,one component is working and another component is colded at the begining.Each component has k failure states and a working state.Using a replacement strategy based on the number of faults of component 1.Using update reward theorem,the average cost per unit time of the long-term operation of the system is derived and the effectiveness of the model is illustrated by a numerical example.