Performance evaluation of a repairable system by using hesitant normal lambda-tau methodology

The main purpose of the present paper is to put forward a new methodology called “Hesitant Normal Lambda-Tau Methodology” for obtaining the reliability indices of complex systems. The new methodology integrates the Hesitant Fuzzy Set (HFS) theory and the normal membership function with the Lambda-Tau methodology for system performance evaluation. The HFS theory is used to represent the failure rate (λ) and repair time (τ), as it uses imprecise and uncertain data for calculating reliability indices. The system’s Petri-Nets (PN) model is used to generate minimum cut and path sets, which are then used to calculate λ and τ of the PN model’s top position using the proposed methodology. The boiler air circulation system of a thermal power plant has been considered to exhibit the proposed methodology. The failure rates of the system are considered to follow an exponential distribution. Various expressions of reliability measures, such as mean time to failure, mean time to repair, mean time between failures, reliability, availability, and expected number of failures, are obtained, and numerical values with different spreads are calculated and tabulated.