Reliability Analysis Of Three Components Standby System

Standby repairable system is one of important model in the reliability research. Basedon the references, the paper has submitted the priority, the PH distributions and therepairman vacation issues into the repairable model, and we obtain the reliability indexesof these systems.Firstly, this paper studies the three-dissimilar-unit cold standby repairabledeteriorating system with priority in repair and use. Assume that the working time and therepair time distributions of the three components are exponential distribution, the repair ofcomponent2is geometrical repair and the repair of component1and3is as good as new,but compared with component3, component2are given priority in repair and use. Underthese assumptions, using the geometric process and the method of supplementary variable,it is obtained that some system reliability indices such as the system availability, ROCOFand the idle probability of the repairman are educed. Effective of the results is verified viaa numerical example.Secondly, this article studies three-dissimilar-unit cold standby repairabledeteriorating system with a single repairman vacation and priority．Assume that threecomponents of the working time and the repair time are subject to the differentexponential distributions and the repairman vacation time is a general continuousdistribution, furthermore, the component1and2become stipulated for its priority in useand repair. It is assumed that the component1is not “as good as new”, but the repairs ofthe component2and3are “as good as new”. By using the geometric process theory, thesupplementary variable method and the Laplace transform tool, availability and reliabilityof the system and other reliability indices are obtained. Finally, a numerical example isgiven to verify the correctness of the results.Thirdly, this paper deals with warm standby repairable system consisting of threedissimilar units and one repairman．Assume that three components of the working timeand standby time are subject to the different exponential distributions, the repair time afterfault, the repair time after standby and the repairman vacation time are general continuousdistributions. By using Markov process theory and the supplementary variable method, explicit expressions of some reliability indexes of the system is given.Finally, a warm standby system which the repair time of the two components are PHdistributions is studied. Assume that two components of the working time and standbytime are subject to the different exponential distributions, the repair time after fault and therepair time after standby are PH distributions. By using the supplementary variable andthe generalized Markov progress, some reliability indexes of the system are obtained.