Reliability Analysis Of Warm Standby Repairable Deteriorating System With Not As Good As New

Reliability analysis of the repair non-new for repairable system is one of important inthe reliability research. In repairable model, the warm standby system is a very importantmodel. Based on the references, the paper has submitted the priority and the repairmanvacation issues into the repairable model, and we obtain the reliability indices of thesesystems.Firstly, the repair non-new of two different components for the warm standbydeteriorating system is studied. The work failures and standby failures are different in thesystem. The component1is not as good as new, and the component2can be repaired asgood as new. By using the geometric process theory, the supplementary variable methodand the Laplace transform tool, we get the system reliability and mean time to first failureof expression. A numerical example is given to illustrate the theoretical results of themodel.Secondly, reliability analysis of the repair non-new for the warm standby repairabledeteriorating system with the priority and repairman single vacation of both cases arestudied, respectively.(1) The repair non-new of two different components for the warmstandby system is introduced priority. The component of working life and the failure repairtime are exponentially distributed. The component1is not as good as new and has thepriority in repair and in use, and the component2of repair is as good as new.(2) Therepair non-new of two different components for the warm standby system is introducedthe repairman vacation. The component of working life and the failure repair time areexponentially distributed, and the repairman vacation time is subject the generaldistribution. The component1is not as good as new and the component2is as good asnew. In these assumptions, by using the geometric process theory, the supplementaryvariable method and the Laplace transform tool, we obtain Laplace transform formula ofsome reliability indices of these two systems such as availability, reliability and system'sfirst failure the average time. A numerical example is given to illustrate the theoreticalresults of the model.Finally, based on the above types of the warm standby system, a warm standbyrepairable deteriorating system for the generally distributed of the repair times withrepairman vacation is studied. The repair of the system components are not as good as new,the components of working time and repairman vacation are subject to the different exponential distribution and the repair time is subject to general distribution. By using thegeometric process theory, the supplementary variable method and the Laplace transformtool, the reliability of some important indices such as system availability, reliability, andthe transient failure frequency of the system are obtained. A numerical simulation is usedto verify the effective of the results.