Reliability Analysis Of Repairable System With Set-up Time

The repairable system repairman ready repair time is extension and development ofthe repairable system repairman vacation. The model of repairable system repairmanvacation is more common system model in the repairable system. Repairman has readyrepair time can have the important influence to the system reliability expressions and theeconomic benefit of the system. Therefore, it has the important significance and theapplication value to consider that repairman has set-up time and multiple vacations.This paper studies three repairable system models with set-up time and multiplevacations of a repairman. These are new ones, which are the spread of the related modelsin the current references and have the important research value.Firstly, a n-unit series repairable system with repairman has set-up time and multiplevacations is studied. Through the analysis of the system model, we give the mainreliability index of the system steady-state, and the Laplace transform type of theinstantaneous availability and the instantaneous fault frequency by using the method ofsupplementary variable method, the vector Markov process method and the tool of theLaplace transform. We also analyse a special case.Secondly, we study a two-unit parallel repairable system with repairman has set-uptime and multiple vacations is studied. Through the analysis of the system model, byusing supplementary variable method, we obtain the definitions of system states. Thenwo obtain the Laplace transform type of the instantaneous availability and theinstantaneous fault frequency, and the reliability index of the steady-state availability, thesteady-state fault frequency and the vacation probability by using the vector Markovprocess method and the tool of the Laplace transform. In addition, we also carry on thenumerical analysis to the system partial reliability indices.Finally, we discuss a three-unit series-parallel repairable system with repairman hasset-up time and multiple vacations. Through the describe and assumptions of the systemmodel, by using the method of supplementary variable method, the vector Markovprocess method and the tool of the Laplace transform, we obtain the Laplace transform type of the instantaneous availability and the vacation probability.