On Stochastic Properties Of The Condition Standby System

Redundant system is main object of reliability mathematics.Warm standby system,cold standby system,hot system and load-sharing parallel system are all typical redundant systems.They have been widely used in many fields.This paper includes three parts.In the first part,we mainly study the stochastic comparisons of a general standby system with one standby component and two active units.It is concluded that the performance of the load-sharing parallel system is better than the warm standby system,the performance of the cold standby system is better than the warm standby system,and the performance of the cold standby system is better than the hot system in the sense of certain stochastic order.In the second part,we investigate the optimal allocation of standby to a general standby system.Firstly,we discussed the optimal allocation problem of a single standby component in a series system of two or three separate components.It is possible to improve the performance of the system by assigning the warm standby component to a working component with larger hazard rate order or reversed hazard rate order.Secondly,we investigate the optimal allocation problem of one of two general standby in a series system one with two independent components.Finally,we investigate the optimal allocation of a single standby in a parallel system with two independent components.In the sense of stochastic precedence order,a warm standby is distributed to the stronger active unit of the parallel system is proven to be better than the warm standby is distributed to the weaker active unit.In the third part,we investigate the stochastic comparison between a system of used components and a used system in the series system or parallel system.Cases of residual life and inactivity time are investigated,respectively.