Some Stochastic Properties Of The Load Sharing Parallel System

In reliability research,in order to improve the reliability of the system,redundant components are usually configured in the system to form redundant systems.Hot standby system,cold standby system and warm standby system are common redundant systems.The load sharing system is an extension of the redundant system,in which when one active component in the system fails,its load is assigned to the remaining surviving components.The load sharing parallel system would be the warm standby system in some conditions.In a redundant system,the reliability of the system will be affected by the difference of redundant components and the configuration of different positions in the system.Therefore,reasonable selection of redundant components and appropriate configuration location is the focus of the redundant system research.In this paper,some stochastic properties of the load sharing parallel system are studied by stochastic comparison.In the first part,some stochastic properties of the load sharing parallel system consisting of exponential distributed components are studied.On the one hand,a load sharing parallel system consisting of an active component and a load standby component is considered.When load standby components are the same and active components are different,the stochastic comparison between two corresponding load sharing parallel systems in the usual stochastic order is established.When load standby components,active components are different,the stochastic comparison between two corresponding load sharing parallel systems in the hazard rate order is established.On the other hand,the optimal allocation of a load standby component in a series or parallel system composed of two components is discussed.Some results are obtained.In the series system,the system reliability is better if the load standby component is allocated to the weaker component in the hazard rate order.In the parallel system,it is better if load standby component is allocated to the stronger component in the reversed hazard rate order.In the second part,some stochastic properties of the warm standby system are studied.Firstly,a warm standby system consisting of an active component and a redundant component is considered.In the two cases where active components are the same or different,when redundant components are different,the stochastic comparison between two corresponding warm standby systems in the usual stochastic order is established.Secondly,by comparing the reliability functions of two redundant components configured respectively to different active components in the series or parallel system,the optimal allocation of redundant components is obtained.Finally,the load sharing system is compared with other redundant systems under certain conditions.In addition,some conclusions of the paper are illustrated with examples.