To flexibly evaluate performance and reliability of a real-time system which is intrinsically characterized by stringent timing constraints to generate correct responses, we propose fuzzyrandom variables and build a discrete event model embedded with fuzzy-random variables. Also, we adapt fuzzy-variables to a path-space approach, which derives the upper and lower bounds of reliability by using a semi-Markov model that explicitly contains the deadline information. Consequently, we propose certain formulas of state automata properly transformed by fuzzy-random variables, and present numerical examples applying the formulas to RTP(Rapid Thermal Process) to show that a complex system can be properly evaluated based on this model by computer simulation.