University of Calicut

13 August 2020

Reliability analysis of a multi state system with common cause failures using Markov Regenerative Process

Failures of multiple components of a system due to a common cause is called Common Cause Failures (CCF). CCF is the one of the most important issues in evaluation of system reliability. When compared to random failures, which affect individual components, the frequency of CCF has relatively low expectancy. According to Rausand and Hoyland [11] common cause failures is a dependent failure in which two or more component fault states exist simultaneously or within short time interval and are direct result of a shared cause. Beta(β) factor model is the most commonly used model for common cause failures of the multi state system [3]. The β factor model describes the correlation between the independent random component failures and common cause failures in a redundant multi state system. A set of powerful techniques that proved for the solution of non-Markovian models is based on the ideas grouped under the Markov renewal theory. The application of Markov renewal theory for finding reliability and availability of stochastic systems is discussed in [6]. Semi-Markov process is the most widely used and adopted non-Markovian model for evaluating reliability and availability of multi state system. A good reference on the semi-Markov process (SMP) is [8] which discusses the the theory of SMP very clearly, also gives examples which helps to understanding the theory and how to apply the model in many real life situations. The stationary character of Markov regeneratve process (MRGP) has been studied in [10]. Most of the theoretical foundations of Markov regeneratve process (MRGP) were discussed in [2] in which it is named as semi regenerative process. One of the first paper which consider semi-regenerative processes is in Russian (refer [13]). For a concise review on Semi- regenerative, decomposable Semi-regenerative Processes and their applications one may refer to [12]. The transient and steady state analysis of stochastic petri nets are discussed analytically and numerically in [1]. MRGPs have been used to evaluating reliability and availability of the system.

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