Reliability Analysis Of A Repairable System With A Warm Standby Unit And Repairman Vacation

Reliability analysis of repairman vacation for repairable system is one of importantcontent in the reliability research. The system with one warm standby unit is a veryimportant model in the repairable model.This paper submitted the priority, replaceablefacility, dependent components and repair non-new issues into the repairable model andwe obtain the reliability indices of these system.Firstly, the reliability analysis of warm standby system with multiple delay vacationsand component with priority is studied. The work failure, the standby failure, the repairtime after work fault and the repair time after standby fault are different. Component1haspriority in use and repair. By using the supplementary variable method Markov processmathematical theory and Laplace transform. The reliability of some important indices suchas system availability, reliability and system average working time to first failure areobtained. The results have some theoretical and parctical significance.Secondly, a warm standby repairable system with a replaceable facility and repairmanmultiple delay vacations is studied. Assume the repair time after fault and the repair timeafter standby fault of two components, the repair facility’s repair time and repairmanvacation were subject to the general distribution and the other were subject to the differentexponential distribution. By using the supplementary variable method and Laplacetransform, some reliability quantities of the system, such as availability, reliability, thesystem average working time to first failure and other reliability indices are obtained.Finally, two situations of degradation system model with a warm standby componentand repairman vacation are studied.(1) A deteriorating system consisting of three differentcomponents and a single repairman is studied. Component1and3are series, andcomponent2is the warm standby component of component1. The component can bestipulated for its priority in repair and use. The repair of that three components havegeometry and as good as new.(2) In the deteriorating system, component1andcomponent2are dependent components, and the working life of component1and2obedience two-dimensional exponential distribution. Component3is the standbycomponent in the system. The component can be stipulated for its priority in repair and use. The repair of component1is geometry and component2and3are as good as new.Under these assumptions, by using the geometrical process the Laplace transform tool andthe supplementary variable technique, we derive some important reliability indices such asthe system availability, reliability and mean time to first failure. Finally, a numericalexample is given to verify the effective of the results.