Technological limitations of the Markov method for dependability analysis

Abstract

Aim. To identify and classify the technical limitations of the Markov method of system dependability analysis, to define their boundaries taking into account the actual feasibility of the method, to show the opportunities of expanding the applicability of the Markov method. The paper examined the limitations associated with the automation of state graph construction and the mathematical solution of the corresponding systems of algebraic and differential equations using software. Methods. An approach is proposed to automatically constructing state graphs of technical systems defined by a structural diagram of dependability, as well as communication networks defined by a structural diagram. The paper examines approaches to reducing the dimension of a state graph that do not reduce the accuracy of dependability indicator calculation. The author also considers ways of reducing the dimensionality of a state graph by means of truncation or merging inoperative states that cause biased calculated dependability values. Results. The actual limits of applicability of the Markov method are shown along with their relevance in the context of modern information technologies. Approaches are shown that expand the applicability of the Markov method for analysing the dependability of large systems. The existing approach to state graph truncation were examined. Approaches to merging inoperative graph states were proposed and investigated (for bias). Conclusion. The approaches discussed in the paper allow extending the applicability of the Markov method of system dependability analysis to systems with a larger number of subsystems.