A two identical unit standby system with inspection, two types of repair and delayed replacement of standby

Abstract

The paper deals with reliability and profit function analysis of a two identical unit standby system model with two modes- Normal and Total failure of each unit. Initially one unit is operative and the other is kept into cold standby. Upon failure of the operative unit the standby unit takes a random time to replace the operative unit. The time is called the delay time for replacement of the operative unit. Inspection is required to detect the type of failure after which the type of repair (either Type-1 or Type-2) is made. Whenever, the operative unit fails, a repairman is called to come at the system for the replacement of failed operative unit with standby and he takes some significant time to reach at the system. Failure time distribution is taken as exponential. The repair and inspection time distributions are also taken as exponential. Whereas the arrival and replacement time distribution are taken as general. By using supplementary variable technique, the various important measures of system effectiveness have been obtained. © 2019 DAV College. All rights reserved.