SEMI-MARKOV RELIABILITY MODELS

Abstract

Traditional technologies for reliability analysis of semi-Markov systems are limited to obtaining a stationary state probability distribution. However, when solving practical control problems in such systems, the study of transient processes is of considerable interest. This implies the subject of research - the analysis of the laws of distribution of the system states probabilities. The goal of the work is to obtain the desired distribution at any time. The complexity of the problem solving is determined by the need to obtain a result for arbitrary distribution laws of the duration of the system's stay in each state before leaving. An easy-to-implement method for the analysis of semi-Markov reliability models has been suggested. The method is based on the possibility of approximating probability-theoretic descriptions of failure and recovery flows in the system using the Erlang distribution laws of the proper order. The developed computational scheme uses the most important property of Erlang flows, which are formed as a result of sieving the simplest Poisson flow. In this case, the semi-Markov model is reduced to the Markov one, which radically simplifies the analysis of real systems.