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An algorithm for integrating uncertain parameters in Markov analysis is proposed. Fuzzy Markov models for aging equipment and substations are developed in which the transition rates/probabilities with uncertainty are represented by fuzzy membership functions. An extension principle and nonlinear optimization-based approaches are utilized for calculation of fuzzy reliability indices. Sensitivity studies for analyzing the impact of various fuzzy membership functions on reliability indices are provided, and the characteristics of the results are discussed. The fuzzy Markov model presented in this paper has valuable application in extending current Markov analysis with the ability to incorporate uncertainties associated with data collected on maintenance activities, etc.