Fuzzy Markov Model for Determination of Fuzzy State Probabilities of Generating Units Including the Effect of Maintenance Scheduling

Abstract

This paper presents a fuzzy Markov model to efficiently incorporate the influences of maintenance scheduling as well as aging of generating units on failure-repair cycle for computation of state probabilities. The proposed model, different from conventional models that are based on a probabilistic approach, employs a fuzzy set concept together with a probabilistic Markov model. This model incorporates fuzzy mean time to failure (FMTTF) and fuzzy mean time to repair (FMTTR) instead of crisp (expected) values for capturing the generating unit uncertainties more effectively through expert evaluation. The fuzzy state probabilities are computed from FMTTF and FMTTR values using fuzzy arithmetic operations for evaluation of the reliability index, fuzzy loss of load probability (FLOLP). Case studies for the maintenance scheduling of a captive power plant catering to an aluminum smelter have been formulated to demonstrate that fuzzy state probabilities as well as FLOLP provide a better explanation than the respective crisp counterparts.