Continuous-time Markov chains is an important subclass in stochastic processes, which have facilitated many applications in business decisions, investment risk analysis, insurance policy making and reliability modeling. It should be fully aware that the existing continuous-time Markov chains theory is merely an ideology under which the random uncertainty governs the phenomena. However, the real world phenomena are often revealing the randomness and vagueness co-existence reality and thus the probabilistic continuous-time Markov chains modeling practices may be not adequate. In this paper, we define the random fuzzy continuous-time Markov chains, explore the related average chance distributions, and propose a scheme for the parameter estimation and a simulation scheme as well. It is expecting that a foundational work can be established for reliability modeling and risk analysis, particularly, repairable system modeling.
