System Reliability And Availability Analyses Based On Markov Processes

Reliability indexes is an important basis for quantitative evaluation of system performance.The main reliability indexes of the system include the first time to failure,the availability of the system,the average fault number in a given period of time,the average start time and the average shutdown time.However,the traditional reliability indexes cannot meet the requirements of practical application,so the important work in this paper is to construct a series of new indexes based on the models on Markov repairable systems aggregated stochastic processes.Therefore,the reliability models of two-dimensional and high-dimensional balanced system have been established based on Markov system.The research of this dissertation mainly includes the following aspects:First,the new point availability and new interval availability indices of the Markov repairable systems are established under the given fixed time threshold.The establishment of these indexes is based on the theoretical model of Markov repairable system,which not only requires the system to work at a given point or in a given interval,but also requires the system to work in a longer interval containing a given point or interval.According to the Markov repairable systems model,the specific expression of the reliability indexes is derived by using the ion channel theory and the aggregated stochastic process theory.The new indexes are compared with the traditional one,then some properties of the new indexes are obtained.Secondly,the new point availability and new interval availability indexes of the Markov repairable system with random threshold are established.The establishment of these indexes is based on the theoretical model of Markov repairable system,which not only requires the system to work at a given point or in a given interval,but also requires the system to work in a random interval containing a given point or interval.According to the Markov repairable system model,the analytic expression of the availability indexes in this situation is derived by using the ion channel theory and the aggregated stochastic process theory.Thirdly,the theoretical model of two-dimensional and n-dimensional balanced system under Markov environment is constructed,and the reliability indexes of the model are given.The two-dimensional balanced system is composed of two independent Markov processes.The condition of its balance is that the absolute value of the state difference of the two Markov processes is not greater than the given threshold value,and the state value of both Markov processes cannot be greater than a given threshold value.According to the theory of ion channel and the theory of polymerization random process,the analytical expression of the reliability indexes of the balanced system is derived by using the Kronecker sum,Kronecker product and Laplace operator in matrix algebra.Fourthly,a series of new first passage time indexes under Markov environments are established.The establishment of these indexes are based on the Markov repairable system theory.The new first passage time indexes include the following situations:(1)not only the system reaches the given state,but also to stay in the state longer than the given threshold;(2)the system is required not only to reach the given state,but also to remain in the state for less than the given threshold;(3)it is not only required that the system reaches the given state and its sojourn time is less than the given threshold value,but also that the sojourn time in the previous state is greater than the given threshold value;(4)it is required that the system is greater than the given threshold value in a given state for continuous k times;(5)the system is required to be longer than the threshold totally for k times in a given state.The expression of the new indexes is obtained by using ion channel theory,aggregated stochastic process theory and Laplace operator.This study has important theoretical and practical significance for the research of reliability indexes.In this dissertation,not only a new balanced system model is constructed,but also a new aggregate stochastic process is presented.The new model can promote the application of ion channel theory and aggregated stochastic process in reliability.A series of new indexes constructed in this dissertation can not only enrich the content of reliability indexes,but also expand the research scope of reliability,which provide theoretical basis for the maintainability optimization design,reliability assessment and management of Markov repairable system.