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Reliability analysis of a two-unit standby system by computer simulation

We study the two-unit standby system with repair and with preventive maintenance. Preventive maintenance is introduced in order to make the lifetime of the system longer. Using Monte-Carlo method we simulate the work of the two-unit system and we analyze the influence of different types of preventive maintenance on reliability of the system. | Yugoslav Journal of Operations Research 13 (2003), Number 1, 85-94 RELIABILITY ANALYSIS OF A TWO-UNIT STANDBY SYSTEM BY COMPUTER SIMULATION* Tatjana DAVIDOVI], Slobodanka JANKOVI] Mathematical Institute, Belgrade, Serbia and Montenegro Abstract: We study the two-unit standby system with repair and with preventive maintenance. Preventive maintenance is introduced in order to make the lifetime of the system longer. Using Monte-Carlo method we simulate the work of the two-unit system and we analyze the influence of different types of preventive maintenance on reliability of the system. Monte-Carlo method enables us to find estimates of various parameters relevant to the system for which there exist no explicit formulas in the literature. Keywords: Reliability, two-unit standby system, maintenance, Weibull distribution, simulation. 1. INTRODUCTION In Reliability Theory systems consisting of two units with repair and preventive maintenance were investigated by methods of embedded semi-Markov processes or by recurrent equations which gave formulas, in terms of Laplace transforms, for some random variables which characterize the work of the system. There exists extensive bibliography concerning this topic (see [1], [2], [7], [8]), and the interest to investigate various variants of two-unit systems continues ([3], [4], [5], [11], [15]). Two-unit standby system with repair is important from a theoretical point of view too, because it stimulated the study of limit theorems for a random number of random variables, which appear naturally in this context. Chapter 2 of a recent monograph [10] has the title: ''Doubling with repair'' and it deals with a mathematical model of a two-unit system and with limit theorems related to it. Similar problems are investigated in [6], [9], [12], [13], [14], too. Also, in connection with the two-unit standby system, the possibility of accelerated repair and preventive maintenance (by employing more staff, for instance) and the situation .