METHOD OF HIGH-ORDER MARKOV CHAIN REPRESENTATION THROUGH AN EQUIVALENT FIRST-ORDER CHAIN FOR SOFTWARE RELIABILITY ASSESSMENT

Abstract

Modern complex technical systems, including but not limited to embedded, IoT and telecommunication systems are computer devices in which software plays a significant role. The wide use of such systems for critical applications in terms of failures increases the requirements for reliability and safety of both such systems in general and their software component. At the same time, the complexity of such systems is constantly increasing. To increase the certainty and accuracy of assessing the reliability of modern complex technical systems, it is necessary to use reliability models with a high degree of adequacy. Among the software reliability models, architectural models based on high-order continuous-time Markov chains have a high degree of adequacy. However, the practical use of such models for systems with many states is complicated due to the lack of practical methods and algorithms for calculating the characteristics of such systems. This paper solves the problem by presenting such models in the form of equivalent first-order Markov processes. The paper describes a method for representing a high-order Markov process in the form of an equivalent first-order process with additional virtual states. The proposed approach makes it possible to integrate high-order reliability models into the existing software tools for the analysis of reliability indices of complex technical systems.