Reliability Study Of State Aggregated Repairable Systems With A Repairman Having Vacations Based On Phase-type Distributions

Multi-state systems are one of the hot topics in the reliability theory.It overcomes the limitation of binary state systems which only has two states of working and failure,and is more appropriate to describe the systems composed of multi-state components with different operation levels and different failure modes.Thus,multi-state systems have been widely used in many fields,such as mechanical engineering,computer and network engineering,power systems,aeronautical systems,supply and demand systems and so on.Previous studies of multi-state systems assumed that the lifetimes of the components of the system,the repair times of the failure components are exponentially distributed,or extensions of it,such as Erlang distribution,Weibulll distribution,Gamma distribution,and so on.When there are no failure components in the system,the repairman is idle,which leads to the little application scope of the research results.In fact,the failure rate of components whose lifetimes are exponentially distributed is constant,which neglects the cumulative effect of lifetimes decreasing of components due to using.When the repairman is idle,the human resources are wasted greatly.Thus,it is important for reliability theory and engineering practice to develop state aggregation repairable system models with repairman having multiple vacations based on phase-type(PH)distribution.On the basis of repairman's vacation strategies,random times are governed by PH distribution,and the dependence of occurrence of successive events is governed by Markovian arrival processes(MAP),state aggregation repairable system models with repairman having multiple vacations based on PH distribution are developed in the dissertation.The reliability for the developed system models are evaluated by employing aggregated stochastic process theory,matrix approaches,and Kronecker operator theory.The main innovations of this dissertation are as follows.Firstly,a two-unit cold standby multi-state repairable system model with a repairman having multiple vacations is developed in the continuous time case and the discrete time case,respectively.Some reliability indexes for the system,such as availability,reliability,the rate of occurrence of failures,working probability of the repairman,mean time between the consecutive system failures,conditional probability of failure,are also obtained.Secondly,a two-unit cold standby multi-state repairable system model with multiple vacations and vacation interruption is developed in the continuous time case.Some reliability indexes for the system,such as availability,reliability,the rate of occurrence of failures,working probability of the repairman,mean time between the consecutive system failures,are also obtained.Thirdly,a multi-unit multi-state warm standby repairable system model with multiple vacations and ? shocks is developed in the continuous time case.Some reliability indexes for the system,such as availability,reliability,the rate of occurrence of failures,working probability of the repairman,mean time between the consecutive system failures,are also obtained.Fourthly,a multi-unit multi-state warm standby repairable system model with multiple vacations and N-policy is developed in the continuous time case.Some reliability indexes for the system,such as availability,reliability,the rate of occurrence of failures,working probability of the repairman,mean time between the consecutive system failures,are also obtained.Reliability performance measures for the multi-state repairable system models with repairman having multiple vacations based on PH distribution are obtained.Some reliability indices of the multi-state repairable system models in the transient and steady state are computed by employing matrix approaches,and the validity and rationality of the models are verified by employing numerical examples.The research of this dissertation has important theoretical value and engineering application value.The results of this dissertation can not only push the development of multi-state repairable system models with a repairman having multiple vacation and stochastic process,but also provide decision-making for complex equipments by improving reliability modeling and evaluation,reliability optimization design,maintenance and warranty management.