System Reliability Modeling And Assessment Under Discrete Time Dynamic Environments

Reliability,as an important quality attribute of product,not only is considered as an assessment indicator of major national defense projects by the international military power,but also becomes a key factor for people's livelihood.Furthermore,reliability theory and methods of system modeling and assessment are not only the basis of reliability theory and engineering,but also the premise of reliability work.In practical engineering applications,however,some factors,such as changing environments,missions,and multiple criteria,present some new and significant challenges to reliability theory,especially reliability modeling and assessment under a static environment.In this thesis,we mainly carry out the research on the issue of system reliability modeling and assessment with the dynamic environments changing.Based on the discrete-time discrete-state system,we consider the effects of cyclic or random missions or environments,multi-failure criterion,multiple states etc.on the system,establish the corresponding novel reliability models,and put forward some new reliability indexes.Also,the calculation formulas of a variety of reliability indexes are derived,the probability distributions of some sojourn times are calculated,and the reliability evaluating methods are proposed.The detailed research works of this thesis are including:Firstly,based on discrete-state non-repairable systems,a discrete-time reliability model of Markov systems is developed by considering the cyclic environment changing and two failure modes,and by using the Markov chain theory and Z-transform.In this new model,we deduce the closed form solutions of some reliability indexes such as reliability function,average lifetime and failure rate function etc.,and obtain probability distributions of some sojourn times with perfect and two types of imperfect functions.Three models of valve systems are discussed in details based on different reliability structures,and a numerical example is also presented by applying our proposed methods for two special cases.Secondly,based on discrete-state non-repairable systems,a discrete-time reliability model of semi-Markov system is established by considering the cyclic environment changing and multiple failure modes,and by using the aggregated stochastic processes theory,the semi-Markov chain theory and Z-transform method.In this new model,the formulas of some indexes such as reliability function,average life expectancy and failure rate function etc.are deduced.Again,we obtain probability distributions of sojourn times with perfect and imperfect functions.Finally,the detailed calculation process and numerical examples are given by taking the negative binomial distribution and the geometric distribution as the special cases.Thirdly,based on discrete-state repairable systems,a discrete-time reliability model of Markov system in random environments is proposed by considering the random environment changing and multiple states,and by using the aggregated stochastic processes theory,the Markov chain theory and Z-transform method.Also,the formulas such as system reliability,environmental reliability,point or interval availabilities,multi-point or multi-interval availabilities and so on are easily obtained with the closed form solutions.In addition,the probability distributions of some sojourn times we are interested in are deduced.Finally,the model of “ k-out-of-n :(F)” with Markov environment-switching is demonstrated the reliability evaluating method.Finally,a case study of project application is carried out.Taking a ship power station system as an example,the reliability model of the system is studied under the conditions of normal driving,berthing,entry and exit.Different working conditions,different system structures and different reliability criteria result in different clustering ways of some states.A series of reliability indicators,such as system reliability,condition reliability,single-point availability of the system,multi-point availabilities of the system at different time points,etc.,are obtained for the description of the ship's power plant system.Some probability distributions of some sojourn times are also calculated.These methods and conclusions provide the theoretical support and economic benefits for shipbuilding industry.The methods of system reliability modeling and assessment under the dynamic environments studied in this thesis have important theoretical and practical significance.This research is more in line with the actual requirements and needs.The proposed models and methods for modeling and calculations enrich the reliability theory and its connotation,expand the application scopes,and provide effective theoretical supports for maintenance and decision-making etc.in practical application.New models and methods are also helpful for the other branch of management science and engineering field.