Improved Availability Index for Repairable Fuzzy Multi-State Systems

Abstract

Fuzzy multi-state systems (FMSSs) comprise FMS components (FMSCs) aims at analyzing non-probabilistic uncertain circumstances defined by fuzzy state-transition rate and performance numbers. The triangular fuzzy number that features intuitive and algebraic operations is widely used for quantifying fuzziness. This study aims to overcome the drawbacks of the existing FMSS availability index that either does not conform to a normal convex set or is inconsistent with the crisp-circumstance multi-state system (MSS) availability beyond summation over state probabilities that do no equal unity. The proposed method first evaluates the instantaneous state probability (ISP) of FMSCs by establishing the FMSCs Markov model. Subsequently, the FMSSs ISP is evaluated by integrating the FMSCs ISP using the fuzzy universal generating function based on the system-structure function. A "constrained nonlinear parameter programming model" has been developed to evaluate the improved FMSSs availability. The corresponding availability index features the normal convex set whilst fulfilling the MSS theory, which requires state probabilities to equal unity during availability evaluation. The effectiveness of the proposed approach has been verified using an illustrated community-based smart-grid system comprising three FMSCs-solar-and wind-energy systems as well as diesel-generator equipment. Moreover, the results of an independent sensitive analysis provide further insights into the improved FMSSs availability with regard to the time and circumstance fuzziness.

Condition-Based Multi-State-System Maintenance Models for Smart Grid System with Stochastic Power Supply and Demand

“…Huang et al [18] established a condition-based multi-objective MSS preventive maintenance model using CTMC to evaluate the MSS performance in terms of the mean system unavailability and total maintenance cost, which considers a human reliability factor associated with maintenance personnel. Chen et al [19] pioneered a novel fuzzy MSS availability using probability theory and uncertainty theory to define the MSS features of random uncertainty, where the state probability and performance of system components are non-probabilistic uncertain variables.…”