An inspection- repair-replacement model of a stochastic standby system with server failure

Abstract

The complexity of engineering systems makes it challenging to keep them functional without failures for longer interval of time. This task is achieved by adopting effective maintenance strategies and appropriate structure design. So in such cases the functioning of service mechanism and that of the server becomes essential. The server failure during any maintenance activity may lead to declined availability and hence the profit. In this paper we develop a probabilistic model for a standby system consisting of two identical units and a server subject to failure and treatment. The inspection
of failed server reveals feasibility for treatment or replacement. The replacement time of server and switching time of standby is negligible. The failure, repair, inspection and treatment times are assumed as arbitrary. The model is developed using semi-Markov process and the steady state results of interests are derived using regeneration point technique of renewal theory and Laplace transformations. The practical importance of the study is highlighted through numerical simulation, for a particular case.