The Analysis And Replacement Policy For Repairable Systems Under Stepwise Poisson Shocks

The reliability analysis and maintenance policy are two important contents in the theory of reliability,which have been widely investigated.Firstly,among the study on repairable systems,most literature assume that system fails due to either extrinsic factors(shocks)or intrinsic factors(ageing,degeneration),however,system failure may be caused by both of them.Secondly,the arrivals of shocks are mainly assumed to follow a Poisson process,the intensity of which is a constant.In fact,the intensity of the shock may change.At last,the repair on component is assumed to be "as good as new",however,the repair is "imperfect".Based on the existing investigations on shock models,we discuss it more in-depth in this paper.Some explicit expressions of reliability indices are obtained.By using renewal-reward theorem,the explicit expressions of the expected cost rate C(N)and the optimal replacement policy N*under the maintenance policy N are derived respectively,and the existence and uniqueness of the optimal replacement policy N*is proved.Then some numerical examples are given to validate some results in this paper.In this thesis,the main work is listed as follows:Chapter 1 introduces the basic elements and development of reliability theory,and system reliability analysis and replacement policy are mainly included.In Chapter 2,a one-component repairable system under stepwise Poisson shocks is studied.Both intrinsic factors and external factors(shocks)can cause system failure.Assume that shocks arrive according to a stepwise Poisson process,the intensity changes with the failure number of working component.The working component fails when the magnitude of a shock is larger than the threshold of the working component,and the repair is "imperfect".Component’s successive lifetime and successive repair time follow an extended Poisson processes,and the thresholds of the working component under different shocks follow a geometric process.By using Markov process and Laplace transform method,explicit expressions of reliability indices are obtained.By using renewal-reward theorem,the explicit expressions of the expected cost rate C(N)and the optimal replacement policy N*under the maintenance policy N are derived respectively,and the existence and uniqueness of the optimal replacement policy N*is proved.In Chapter 3,a two-dissimilar-component cold standby repairable system under stepwise Poisson shocks is investigated.Some explicit expressions of reliability indices are obtained.Here,we consider a replacement policy based on the failure number of component 1 and component 2.By using renewal-reward theorem,the explicit expressions of the expected cost rate C(N)and the optimal replacement policy N*under the maintenance policy N are derived respectively,and the existence and uniqueness of the optimal replacement policy N*is proved.In Chapter 4,a two-dissimilar-component cold standby system with priority under stepwise Poisson shocks is studied.The underlying assumptions remain unchanged.Assume that component 1 has priority in use and repair.Some explicit expressions of reliability indices are obtained.Here,we consider a replacement policy based on the failure number of component 1 and component 2.By using renewal-reward theorem,the explicit expressions of the expected cost rate C(N)and the optimal replacement policy N*under the maintenance policy N are derived respectively,and the existence and uniqueness of the optimal replacement policy N*is proved.