Reliability Analysis Of Several Repairable Systems With Multiple Vacations And Non-new Repair

Repairable system is one of the important systems in the reliability studies. Multiple vacations and repair of non-new in a repairable system maintenance model is relatively common. Both are closer to reality than single vacation of no vacation and repair as good as new. Based on references, this paper has submitted multiple vacations and repair of non-new into several different models. Got some reliability indicators Laplace expression by use some mathematical tools.Firstly, this pair studies a Gaver’s parallel system attended by a repairman with multiple vacation, two parallel units with repair of new and a cold standby unit with repair of non-new. The repairman vacation time obeys the general distribution. The system’s instantaneous availability, instantaneous reliability and other reliability indices are obtained by using the geometric process theory, the supplementary variable method, Laplace transform and other math tools.Secondly, this pair studies a repairable warm standby system composed of two components and one repairman with multiple vacations. The repairman vacation time obeys the general distribution. The repair of component 1 is not as good as new and the repair of component 2 is as good as new. Based on the premise that the working time, the standby time, the repair time after fault and the repair time after standby fault of two components are subject to different exponential distributions, the Laplace transform expression of system’s instantaneous availability, instantaneous reliability and other reliability indices are obtained by using the geometric process theory, the supplementary variable method, Laplace transform and other math tools.Thirdly, this pair studies a three part series-parallel degradation repairable system with multiple vacations and non-new repair. The time of repairman obey general continuous distribution, so do the repair time of the two same type parallel components. The other series component is geometry repair. The Laplace transform expression of system’s instantaneous availability, instantaneous reliability and other reliability indices are obtained by using the geometric process theory, the supplementary variable method, Laplace transform and other math tools.Finally,a three parts series cold standby degradation repairable system with multiple vacation and non-new repair is studied. Two same type components are cold standby for each other. Their repair time obey to general continuous distribution. The other series component is geometry repair. The Laplace transform expression of system’s instantaneous availability, instantaneous reliability and other reliability indices are obtained by using the geometric process theory, the supplementary variable method, Laplace transform and other math tools.