Failure Detection And Imperfect Preventive Maintenance Strategy Of Reliability System

Imperfect preventive maintenance as one of the most basic maintenance strate-gy,has been extensively studied.However,in the studying of the imperfect preventive maintenance,the inspection policy of systems is seldom considered.In this paper,we study a class of reliability systems,for which the system failures can only be found by inspections.For such a system,periodical inspection procedure is executed to determine the system state,and then preventive maintenance(PM)or replacement actions are performed.Based on the effect of PM on the system state,two types of models,including effective age model and failure rate model,are researched.At first,we discuss the effective age model under imperfect PM(IPM).In the first effective age model,periodic inspection of the system is performed with interval time T.If the system is found at working state,then IPM is executed,and the effective age of the system after IPM reduced proportionally.If a failure is detected in a inspection,then the system is replaced by a new one.Based on the Renewal Reward Theorem,the long-run average cost rate of the system can be calculated,and the optimal inspection policy can be determined by minimizing the long-run average cost rate.In the second effective age model,the PM can be an imperfect PM or a perfect PM determined by a Bernoulli Variable.After a perfect PM,the system is renewed.The problem is to find the optimal inspection policy T.The third model is also a generalization of model one,in which the system is preventively replaced by a new one if the number of IPM reaches N.The objective is to find the optimal bivariate policy(T,N)such that the long-run average cost rate of the system is minimized.The last model considers the periodic inspection,perfect and imperfect PM,preventive replacement and failure replacement simultaneously.The aim is also to determined the optimal bivariate policy(T,N).For the four models proposed,the theoretical results of optimal policies are difficult to derived.So,we adopt numerical method to compute the optimal policies of inspection and preventive replacement.Some comparisons are also provided.Next,we study the failure rate model of the system under IPM.We also perform periodic inspection and IPM for the system.The different is that the effective of IPM is to reduce the failure rate of the system in this type of models.Similar to the work has been done in the effective age model,we also develop four failure rate models,in which the long-run average cost rates are calculated,and the optimal inspection and preventive replacement policies are investigated numerically.