TITLE:
Algorithm to Assess Temporarily Reliability of a System Relying Upon the Intensity of the Failure and Recovery Flows of Three Autonomous Subsystems
AUTHORS:
Victor Kravets, Valerii Domanskyi, Illia Domanskyi, Volodymyr Kravets
KEYWORDS:
Reliability of Systems, Markovian Process, Kolmogorov Equation, State Probabilities
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.15 No.6,
June
13,
2025
ABSTRACT: An algorithm is being developed to conduct a computational experiment to study the dynamics of random processes in an asymmetric Markov chain with eight discrete states and continuous time. The algorithm is based on an exact analytical solution of the Kolmogorov differential equations, derived from the concept of harmonizing the mathematical description of models. The harmonization of the mathematical description is reflected in the asymmetric structure of the possible states of the system under study, which consists of three autonomous subsystems, the symmetric distribution of the roots of the Kolmogorov characteristic equation in the complex plane, the systematic representation of the used matrix tables and corresponding determinant tables. It is shown that presenting expanded formulas in the form of ordered tables allows for a compact description of a large volume of initial data, overcomes limitations related to the problem’s dimensionality, and ensures the algorithm’s adaptability to computer technologies, including the verification challenge. The algorithm is tested on a methodological example assessing the reliability of a military structure consisting of three separate autonomous branches of the armed forces. The probabilities of possible states of the military structure are determined depending on the intensity of loss and recovery flows in the branches. The abstract, dimensionless results of the state probability calculations are interpreted in terms of the physically significant factor—the time of combat readiness of the branches and the military structure as a whole. Verification of the calculation results, the algorithm, and the mathematical model is performed using a time-invariant condition that links the probabilities of the system’s states. A general algorithm for studying asymmetric Markov chains and the corresponding Kolmogorov equations for complex systems is formulated.