The semi-Markov model for the ‘technological module–storage device’ structure

The theory of semi-Markov processes has been used to design a model of a ‘technological module–storage device’ (TM–SD) structure. Stationary characteristics based on the obtained equations were determined to find a stationary distribution of the Markov embedded chain. Relying upon the performed studies, the stationary distribution of a semi-Markov process was determined. This allowed calculating the availability ratio of the TM–SD structure, and the design formula was given. The Markov restoration equations for the TM–SD system with taking into account TM and SD failures were solved assuming the exponential behavior of these failures. The obtained expressions describe how such a system operates and allow substituting the TM–SD system with an equivalent element with two factor states. This result significantly simplifies the modeling problem for more complex systems. The legitimacy of using exponential distributions of random variables (error-free periods for TM and SD) was analyzed. The performed simulation modeling revealed that the hypothesis for an exponential behavior of error-free periods for TM as a whole (and SD as well) can be accepted even in the case when TM (or SD) consists of six nodes.