| Reliability analysis of components dependent for repairable system is one ofimportant content in the reliability research; its application is rather extensive; Reliabilityanalysis of repairman vacation for system model is one of important repairable model.Based on references, this paper has combined unit multi-state, multiple delay vacations,replaceable repair-facility and repair of non-new with components dependent system andwe obtained some important reliability indices of these systems.Firstly, in this paper, we studied a parallel deteriorating system with single repairmanvacation and unit multi-state.(1) Unit1is geometry repair and unit2is as good as new,the repair time subject to exponential distribution.(2) There are two kinds of failure statefor every component, the working time of two components subject to exponentialdistribution. Considering two cases above, the vacation time of repairman is following ageneral continuous distribution. By using the mathematical tools such as the geometricprocess, the supplementary variable method and Laplace transform the reliability indicessuch as system availability, reliability and MTTFF are obtained.Secondly, in this paper, we studied a two same components dependent parallelrepairable system with a replaceable repair-facility and multiple vacations. Assume thatthe working time of two components and repair-facility subject to different exponentialdistribution, whereas the vacation time of repairman, the repair time of unit andreplacement time of facility follow different general continuous distribution. By using thegeneralized Markov equation, the supplementary variable method and Laplace transform,the reliability of some important indices such as system reliability, MTTFF andsteady-state availability are obtained.Finally, we studied a two same components dependent parallel repairable system witha replaceable repair-facility and multiple delay vacations. Suppose that the working timeof two components and repair-facility are subject to different exponential distribution,whereas the vacation time of repairman, the repair time of unit and replacement time offacility is follow respectively a general continuous distribution, by using the vectorMarkov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the reliability of some important indices such as system reliability,Mean Time To First Failure (MTTFF) and steady-state availability are obtained. Finally, anumerical example is given to validate the derived indices. |
