Several Repairable Systems Attended By A Repairman With Vacations And A Replaceable Facility

Repairable system is very important in the research of reliability theory and reliability engineering. On the base of repairable system, the paper has extended some models by considering that the repairman in the system can take single vacations, multiple vacations or multiple delay vacations. The failed units can be repaired by the repair facility, but in fact the facility may fail when it is in working, and then it need to be replaced. It is in keeping with the fact, and it is well worth investigating the system with the replaceable facility and the repairman vacation in the filed of reliability analysis.This paper has researched the reliability analysis of three systems as follows:(1) The two-similar-unit paralleled repairable system with a replaceable repair facility and a repairman who takes a single vacation is studied. It is assumed that the life of the both units and the vacation time of the repairman are exponential distributions, the repair time of the unit, the vacation time of the repairman and the replace time of the repair facility are general continuous distributions. By using the supplementary variables approach and the generalized Markov process method, some important reliability indexes are gived such as the system’s reliability, MTTFF, MUT and the failure frequency of the system and so on. Some numerical results are illustrated for the model.(2)The Gaver’s parallel repairable system attended by a cold standby unit and a replaceable repair facility and a repairman with multiple vacations. It is assumed that the life of the three units and the vacation time of the repairman are exponential distributions, the repair time of the unit, the vacation time of the repairman and the replacement time of the repair facility are general continuous distributions. By using the supplementary variables approach and the generalized Markov process method, some important reliability indexes are derived. Numerical simulation of the steady-state availability and the steady-state failure frequence and the mean-up time are given in the paper.(3) The two-similar-unit paralleled repairable system with a replaceable facility and 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, the vacation time of the repairman and the replace time of the repair facility are general continuous distributions. By using the supplementary variables approach and the generalized Markov process method, some important reliability indexes of the system are obtained. Numerical results are provided to investigate the effect of the steady-state availability and mean up-time as the changing of system parameters.