A Markovian approach to reliability estimation of series-parallel system with Fermatean fuzzy sets

Abstract

Markov process has been an extremely contributive method in the reliability evaluation of electrical systems for the past many decades, as a result, it has been extended by numerous researchers to address various types of issues occurring in different types of engineering systems. However, one thing it fails to address is the fuzziness in real-life systems. This fuzziness or randomness can occur either because of incomplete awareness of the operating conditions or the application of different numerical assessment methods by different operators, causing inconsistency in a system’s assessment. It can be dealt with the incorporation of the concept of fuzzy sets in the reliability analysis. This study aims to incorporate fuzzy sets, specifically, Fermatean fuzzy sets (FFS) with the Markov procedure for assessing the fuzzy reliability, availability, and sensitivity of fuzzy reliability of a system. The described approach is justified with an example of a generic series–parallel system and its fuzzy reliability and availability are computed by Markov modelling where failure rates are characterized by triangular Fermatean fuzzy numbers (TFFN). It is obtained that the behaviour of reliability, availability and sensitivity are the same as in conventional reliability evaluation, thus establishing that the proposed technique is valid. The parameters thus obtained are also depicted both in tabular and graphical forms to achieve conclusive results.