On Availability of a Series system with Imperfect Detectors

Abstract

An n-unit series system with exponential distributions for life-times and repair-time has been considered. Each unit is equipped with a detector to detect failures. Detectors are subject to two failure modes: viz. (i) instantaneous failure i.e. it fails at the time of need when a unit fails; (ii) gradual failure i.e. it fails and gives false alarm for system failure. Steady-state availability of the system is obtained by studying the underlying system equations. Behavior of steady-state unavailability has also been studied analytically.