Stochastic Modeling And Reliability Assessment Of Systems Under External Shocks And Maintenance Actions

To date,reliability assessment of system is an important problem in statistics and engineering and other applied fields.When modelling the reliability characteristics of a system,internal degradation and other external factors may be considered.Generally,the internal factors are predetermined by ex-factory quality of system components,while statistical models to study how external factors act on the lifetime behaviour of the system is attracting more attention in recent years.To this end,the author go through the following three widely mentioned topics.External Shock:Random shocks which lead to sudden changes in the system operation environment are important causes of system failure.Standby Redundancy:Standby redundancy is a technique to improve system reliability and availability,by substituting standby components for broken components.Maintenance Policy:Maintenance actions are intended to improve the condition of the maintained system by restore it to certain operating condition.Therefore,to develop a series of research on reliability modelling,this thesis is composed of three parts corresponding to the above topics.Firstly,efficiently modeling the reliability of system suffering random shocks is an important applied problem.We have studied one of the most representative failure modes,named with cumulative shock model,in which the system is considered failed when the cumulative size of shocks exceed a given level.Phase-type distribution is applied to model the inter-arrival time between shocks and size of damage caused by shocks.It is the generalization of exponential distribution,holding a variety of nice properties.Besides,we have also conducted a series of research on generalized run shock models or mixed cumulative and run shock models,in which the system fails whenever a sequence of specific shocks occurs.Explicit formulas for calculating the system reliability characteristics are presented and numerical examples are also provided for illustrational purpose.In the second and third part,we studied two different maintenance policies in repairable systems.Firstly,we have considered a kind of repairable K-out-of-N system which includes several kinds of standby components.Whenever a working component fails,standby components can substitute for them immediately or after a short warm?up period.Besides,broken components can turn into standby components after repair.The systems are modeled by continuous time Markov chain and the system long run availability is derived.Furthermore,optimal number of warm standby is studied by considering system availability and average long run cost.Lastly,we researched the modeling of imperfect maintenance.We developed an maintenance model,in this model,the recovery extent of the system condition after maintenance is unfixed,they are modeled by several random factors.We refer to the stochastic EM algorithm as the model contains hidden variables.Markov chain Monte Carlo technique is applied in the simulation step in the interation to improve the convergence speed of the EM algorithm.We explored three sampling methods in MCMC procedures,and give a general recommendation by conducting a series of simulation studies and make comparison.In summary,the broad objective of all the three parts is to develop appropriate reliability models when dealing with different types of external factors.All of the underlying models are based on Markovian processes,and can be widely applied in dealing with real world problems.