Evaluation of reliability parameters of a system having three independent components with repair facility

Abstract

Barlow & Prochan [1] were first to study a complex system taking the component failure and repair times as Independent of each other. In recent years, many papers on reliability such as Li  [2] used multi-state weighted k- out- of- n systems to analyze repairable systems with arbitrary failure time distributions. Exponential distribution plays an important role in the study of system with repair. In order to predict and  estimate or optimize the probability of survival and the mean life, it is essential to take exponential distribution.  Earlier, Goel et al[8 ] have done similar reliability analysis taking units in three different modes. Rander et-al [6] has evaluated the cost analysis of two dissimilar cold standby systems with preventive maintenance and replacement of standby units. A pioneer work in this field was done by Gopalan [3] and Osaki [5] by performing analysis of warm standby system and parallel system with bivariate exponential life respectively. Earlier, Pathak et al [10 & 11] studied reliability parameters of a main unit with its supporting units and also compared the results with two different distributions. We define semi-up mode as the case when the one particular unit is not able to operate due to error in other units which makes these units non-operative. In this paper an attempt has been made by authors by incorporating the concept of semi-up mode and tried to obtain the reliability parameters of working system taking three independent components.