A system subject to two risks in a competing risks model is considered.Given the failure of system has occurred at or before x,we introduce the cause reversed failure rate to analyze the probability of a failure in (x-dx,x] and the cause of failure will be the i-th.We give the necessary and sufficient conditions for the independence of system life time and the cause of failure based on caused reversed failure rate.Finally,we study the property of the survival function of inactivity time at time x for the system corresponding to i-th cause of failure.