Set-Valued Markov Chain Dependability Model with Uncertain Data

The development of Markov model approach for probabilistic analysis of dependable systems with uncertain data is considered. Further development of Markov models with interval description of uncertain parameters based on optimization approach to obtaining estimates and ellipsoidal approximations of transition matrices is proposed, which makes it possible to simplify the computational procedures for obtaining boundary estimates for transition and steady-state probabilities of the systems under study. Using the method of Lagrange functions, solutions of optimization problems for obtaining interval estimates of state probabilities are proposed. The proposed technique is illustrated by analysis of cyber-physical system under parametric uncertainty.