Reliability Modeling And Maintenance Strategy For Competing Failure Systems

With the progress and development of science and technology,people’s requirements for products are higher and higher.We not only hope that the product can meet its functional requirements,but also hope that the longer the life of the product,the better,or the fewer failures,the better.The life evolution law of the product can be predicted effectively by reliability modeling and analysis.Furtherly,the established reliability model can provide a basis and guarantee for the maintenance strategy of the product.In practice,many systems or products are affected by multiple failure modes,among which degradation failure and sudden failure caused by random shocks are common.The two failure modes are mutually competing.The failure of the system is caused by the failure mode that happens earlierly.This kind of system is called competing failure system or competing risk system.In real life,competing failure systems are quite common,such as batteries,micro electro mechanical systems,power systems,and so on.Once this kind of system breaks down,it will cause great economic losses.Therefore,it is of great theoretical significance and practical value to study the reliability models and maintenance strategies of competing failure systems.In the paper,taking the competing failure system as the subject of the research,we study the problems of reliability modeling and maintenance strategy optimization.On the one hand,the reliability of the competing failure system is modeled and analyzed by using degradation-based reliability modeling method,shock theory and Copula method.On the other hand,the maintenance strategy of the competing failure system is studied by utilizing delay time model,proportional age reduction model,and so on.Firstly,the reliability model for a competing failure system is developed by considering the dependence between the degradation process and the random shocks.In this paper,random shocks are divided into three types: fatal shock,general shock and small shock,based on which,the reliability model for a competing failure system with high reliability and long life is established.In order to build the reliability model,we assumed that the small shock will not affect the system.The general shocks will not only lead to sudden degradation increment,but also increase the degradation rate of the system.And the fatal shocks will cause the system to fail suddenly.In addition,Copula method is used to solve the dependence among multiple degradation processes.A numerical example is used to verify the validity and accuracy of the constructed reliability model.Secondly,the maintenance modeling for a competing failure system are carried out based on the condition-based maintenance strategy.Reliability modeling and analysis are helpful to evaluate system reliability,while effective maintenance measures can increase the availability of the system in service.In this paper,the competing faiure system is assumed to have the same performance level before failure,that is,the system has only two working states,normal and failed.Based on this premise,the maintainability model is established by using the condition-based maintenance strategy,and the expected cost rate function of the system is constructed.The effectiveness of the constructed maintenance model is demonstrated by taking a series system as the verification object.Then,the maintenance modeling of a multi-state competing failure system are carried out.In fact,the system may have different performance levels in different working periods.The system can be discretized into multiple states if each performance level is regarded as one system state.In this paper,we focus on a three-state(normal,defective and failed)competing failure system,and assume that the inspections for system states are perfect.The maintenance model of the system is established and an example of capacitor bank is given to verify the applicability of the constructed maintenance model.Subsequently,the maintenance modeling of the multi-state competing failure system are carried out by considering the imperfect inspections.In practice,there exist inspection errors due to the limitations of the testing equipment and the technical level of the testing personnel.The maintenance model of a multi-state competing failure system is established under the assumption that the inspection is imperfect.The applicability and effectiveness of the maintenance model are verified by a numerical example.Finallly,the maintenance model is built for the multi-state competing failure system by considering both the imperfect inspections and imperfect maintenance.A preventive replacement is carried out when the defect is detected,which will result in a higher cost.In practice,the cost-effective maintenance can eliminate defects.However,the maintenance behavior can only restore the system to a certain state between “as good as new” and “as bad as old”.That is,the repair is imperfect.In this paper,the maintenance model of a multi-state competing failure system is established by considering the imperfect inspection and imperfect repair for defects.The optimization problem of the maintenance strategy is proposed and the minimization of the expected cost rate in the renewal cycle is realized.The innovations of this paper includes:(1)The shocks arriving at the system is divided into three categories and the Copula method is used to deal with the dependency between multiple degradation processes when building the reliability model of the competing failure system.The proposed modeling method improves the accuracy of the reliability model of competing failure system.(2)This paper establishes the maintenance model of competing failure system based on the condition-based maintenance.The optimal maintenance strategy is obtained by optimizing the maintenance model,which can achieve the purpose of saving maintenance cost.(3)In this paper,the delay time model and homogeneous Poisson process are used to describe the degradation process and the shock process of multi-state competing failure system,and then the maintenance model of the system is established.Furthermore,the maintenance model of the system is reconstructed by considering the inspection error(imperfect inspection)and maintenance degree(imperfect maintenance).The constructed maintenance models can be applied to the multi-state competing failure systems under different working situations.