Reliability Modeling And Analysis For Degradation Repairable Systems Under Dynamic Environments

With the increase of system complexity,the change of system requirements,operating environments,missions and other uncertain factors have put forward serious challenges for system reliability modeling under static situations.In fact,systems degrading in dynamic environments can be widely found in engineering practice.Therefore,it is of great theoretical and practical significance to study the reliability especially the reliability modeling of degradation systems operating in dynamic environments.Inspired by some practical problems,this dissertation focuses on systems degrading in several typical dynamic environments.Degradation models and maintenance models are developed for corresponding systems using the regime switching model and stochastic process theory.Based on these models,system reliability is analyzed and optimal maintenance policies are studied to improve the performance of the system.The main research contents of the dissertation are as follows.Firstly,a model is developed for systems degrading in K cyclical regimes.The distribution of the time to the first failure under this setting is derived and then extended to systems degrading in Markovian environments.When maintenance actions are taken into consideration,a maintenance model is developed under the assumption that the degradation level of the system is continuously inspected.System availabilities are studied in scenarios where environment is dependent and independent with the state of the system,respectively.Secondly,a model is developed for multi-state repairable systems degrading in Markovian environments.The distribution of the time to the first failure is derived.Then an algorithm is presented to simulate the failure time of the system and validate the proposed results.Instantaneous availability and limiting average availability are obtained for systems in the context of continuous and periodical inspections,respectively.In the process of modeling and analysis,system states with the same dagradation rate are classified into the same set by using the aggregated stochastic theory,which can reduce the complexity of the calculation.Thirdly,a model is developed for multi-component systems subject to continuous degradation in the environment with categorized random shocks.An interactive matrix is introduced to describe the interaction among the components.Influences on the components caused by random shocks are defined and classified into three types,which are direct influence,indirect influence and no influence.Then system reliabilities are derived respectively for series systems and parallel systems in a recursive way.To find all the termination conditions of the recursive equations,two algorithms are proposed.With the increase of the number of components,using the recursive method to calculate the reliability of parallel systems may be complex and difficult.To address this problem,an algorithm is proposed to simulate the failure time of the system.Fourthly,a model is developed for systems degrading in dynamic environments subject to several imperfect maintenance actions before each replacement.To describe the system performance,system availabilities including instantaneous availability and limiting average availability,and some time distributions of interest are derived.Then the problem of the optimal maintenance policy is formulated by considering constraints of availability and expected operating times.The existence of the optimal solution is proved and the algorithm of calculation is also presented.Finally,an engineering application case study is conducted.Taking a company which provides excavator rental and maintenance service as an example,the wear process of the bucket teeth which are used in different working environments can be described by the developed models.To depict the performance of the bucket teeth,some reliability indices of interest are derived.In addition,from the manager's point of view,the problem of the optimal maintenance policy with constraints of availability and expected operating times is formulated and then solved by the proposed algorithm,which finally minimum the long term average maintenance cost rate.This dissertation is of important theoretical and practical significance,and its relevant conclusions can be applied to solve difficult problems in modeling systems degrading in various dynamic environments.Moreover,the study also promotes the theoretical development of systems degrading in dynamic environments and provides foundations for reliability analysis,maintenance optimization and decision making,which has strong engineering application value and broad prospects for promotion.