The mathematical model of a non-rezerved renewable technical system developed in this paper can serve as a test model for debugging programs for the automated construction of reliable models of corresponding technical systems.
To calculate the reliability indicators, the reliability data of the elements of the technical system are used as input data. On the basis of these data, a mathematical model of the reliability of the technical system in the form of Kolmogorov-Chapman differential equations is developed, which describe in time the transition process of the technical system from one state to another.
A comparative study of the solution of a Kolmogorov-Chapman’s system using numerical integration methods and using an analytical solution showed no advantages in accuracy and certain advantages in time of the decision on the second approach.
All calculations is made in the system MATLAB.
1. “State standard of Ukraine. Reliability of technology. Terms and definitions.” [“Derjavnyi standart Ukrainy. Nadiynist tehniky. Terminy ta vyznachennia.”] DSTU 2860-94. Official publication — Kyiv Gosstandart of Ukraine. 2. Polovko A. M., Gurov S. V. (2008), “The basics of reliability theory, 2nd ed., trans. and suppl. ” [“Osnovy teorii nadeznosti, 2-e izd., pererab. i dop.”], —- SPB: BHV-Petersburg, 2008.-704 pp. 3. Bobalo Yu. Ya., Volociy B. Yu., Lozinsky O. Yu., Mandziy B. A., Ozyrkovsky L. D., Fedasyuk D. V., Shcherbovskikh S. V., Yakovina V. S. (2013), “Mathematical Models and Methods for Analyzing the Reliability of Radioelectronic, Electrical and Program Systems: Monograph” [“Matematychni modeli ta metody analizu nadijnosti radioelektronnyh, elektrotehnichnyh ta programnyh system: monografia”] — Lviv, Publishing House of Lviv Polytechnic, 2013, 300 pp. 4. Fedoryuk M. V. (1985) “Ordinary Differential Equations — 2nd ed., trans. and suppl.” [“Obyknovennye differenzialnye upavnenia: 2-e izd, perepab. i dop.”] — M.: Science. The main edition of physical and mathematical literature, 1985. — 448 pp. 5. Moler, C. B. and C. F. Van Loan, (1978), “Nineteen Dubious Ways to Compute the Exponential of a Matrix”, SIAM Review 20, 1978, pp. 801–836.