This research is aimed at obtaining a better understanding of how to design expert systems for real-time applications. A metric for a real-time expert system is defined as the probability that the system successfully formulates and executes strategies under real-time constraints. The objectives of the proposed research are to propose a formal theory for quantifying the estimation of this metric and to investigate the validity of the theory by applying it to develop a real-time expert system embedded within a control system with varying degrees of timing requirements. It is expected that the proposed theory can serve as a basis for designing and verifying the functional and timing requirements of future real-time expert systems.