The Reliability Analysis Of Linear Consecutive-(n-1)-out-of-n:G Repairable System With Vacation Of A Repairman

The linear consecutive-k-out-of-n:G repairable system is a very important reliability system.And in the actual case, the components do not just have one failure state. Therefore it is of great practical significance to consider the situation in which the components have many failure states. Meanwhile,it is worthy of study that the repairman have vacation or engage in other work to improve the economic efficiency of the system.This paper is committed to the reliability analysis of linear consecutive-(n-1)-out-of-n:G repairable system,assuming that all the components are the same and life time of each component is exponentially distributed,while the repair time of the components and vacation time of the repairman are both generally distributed,and each component is as good as new after repair.This paper consider the following 4 situations in accordance with the vocation mode of repairman and the failure mode of components :In the first case , a consecutive-(n-1)-out-of-n:G repairable system with single vacation of a repairman is considered .By using the supplementary variable technique , we obtain the differential equations about all the states of the system ,then by using Laplace transform method,we derive the formulas of some main reliability indexes of the system,such as the reliability, the steady state failure frequency etc.In addition,we make initial investigation of the effect by the parameters on reliability indexes through numerical analysis .In the second case , a consecutive-(n-1)-out-of-n:G repairable system with multiple delay vacations of a repairman is considered.Assuming that the delay vacation time of repairman is exponentially distributed,by using the supplementary variable technique we obtain the differential equations about all the states of the system ,then by using Laplace transform method,we derive the formulas of some main reliability indexes of the system, such as the reliability, the steady state failure frequency ,etc.In addition,we make initial investigation of the effect by the parameters on reliability indexes through numerical analysis.In the third case, a consecutive-(n-1)-out-of-n:G repairable system with single vacation of a repairman is considered.Assume that the components in the system are subject to two kinds of failure. By using the supplementary variable technique,we obtain the differential equations about all the states of the system,then by using Laplace transform method,we derive the formulas of some important reliability indexes of the system.In the fourth case ,a consecutive-(n-1)-out-of-n:G repairable system with multiple delay vacation of a repairman is considered.Assume that the delay vacation time of the repairman is exponentially distributed,the components in the system are subject to two kinds of failure . By using the supplementary variable technique, we obtain the differential equations about all the states of the system ,then by using Laplace transform method,we derive the formulas of some important reliability indexes of the system.