An investigation of some conjectures about the hazard rate of warm standby systems

Abstract

Two propositions concerning the comparative behavior of the hazard rate functions for warm, ccld, and hot standby systems are expressed and then examined. The standby systems under study involve two components with constant failure rates. Emphasis is placed on establishing a lower bound on the hazard rate function for a standby system and on developing an optimal employment policy for the use of components in a standby system. A proof is offered to show that the hazard rate function for a cold standby system is a lower bound on the hazard rate function of either a warm or hot standby system. Evidence is then given to support the existence of an optimal employment policy for components in a standby system, but a complete proof is not presented.