Several Repairable Systems Attended By A Repairman With Vacations

Based on the previous research harvest in the theory of reliability, the repairable system has been improved considering the repairman in the system can have a vocation or be engaged in other work when being idle. It has an important influence on the system reliability expressions and the economic benefit of the system. Therefore, it has both theoretical significance and application value to consider the repairable system with repairman vacation.This paper has studied the reliability analysis of several systems as follows:(1) The two-dissimilar-unit paralleled repairable system with multiple delay vacations is studied. It is assumed that the life of the unit and the delay vacation time of the repairman are exponential distributions, the repair time of the unit and the vacation time of the repairman are general continuous distributions. All random variables are separately independent, the unit can be repaired as good as a new one. By using the supplementary variables approach and generalized Markov process method, some important reliability indexes are derived such as the system’s reliability, availability, MTTFF and failure frequency of the system and so on. Numerical simulation is given when the repair time of the component and the vocation time of the repairman have exponential and Gamma distributions.(2) The N-1/N(G) system with multiple delay vacations is studied. It is assumed that the life of the unit and the delay vacation time of the repairman are exponential distributions, the repair time of the unit and the vacation time of the repairman are general continuous distributions. All random variables are separately independent, the unit can be repaired as good as a new one. By using the supplementary variables approach and generalized Markov process method, some important reliability indexes are derived. Numerical simulation is given when the repair time of the component and the vocation time of the repairman have exponential and Gamma distributions.(3) The Gnedenko system with multiple delay vacations is studied. It is assumed that the life of the unit and the delay vacation time of the repairman are exponential distributions, the repair time of the unit and the vacation time of the repairman are general continuous distributions. By using the supplementary variables approach and generalized Markov process method, the Laplace transform of the reliability and the mean time to first failure are attained. Meanwhile, the availability and the failure frequency of the system are obtained. Numerical simulation is given when the repair time of the component and the vocation time of the repairman have exponential and Gamma distributions.(4) On the base of the Gnedenko system with the switch that is always available, we deal with the Gnedenko system with multiple vacations,.the switch is not always available, the lifetime of the switch has0-1distribution, It is assumed that the life of the unit is exponential distribution, the repair time of the unit and the vacation time of the repairman are general continuous distributions, and by using the supplementary variables approach and generalized Markov process method, some important reliability indexes are derived. Numerical simulation is given when the repair time of the component and the vocation time of the repairman have exponential and Gamma distributions.