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This article discusses the residual life and inactivity time of warm standby system at random time. The reliability function of the residual life(inactivity time) of the warm standby system at random time is obtained. And by using stochastic order, we compared the stochastic properties of residual life at different times. Keywords—Stochastic order; warm standby system; Residual life

Order Properties of Conditional Warm Standby System at Random Time