Stochastic Orderings of the Idle time of Inactive Standby Systems

Abstract

In this paper we consider a failed cold standby systems and obtain some stochastic bounds on the
 idle time of such systems. It is assumed that, at a time t the failure of a cold standby system
 is observed, but the actual time of the failure is a time before t. The idle time of the inactive
 cold standby system is measured as the time between the exact time of failure, which is a random
 variable, and time t. We use the idle times of the components of the system to obtain lower and
 upper bounds on the lifetime of the standby system to which they are assembled. We bring some
 examples to show that the results and the conditions imposed to get them are achievable.