Reliability assessment of a series system with redundancy and repair facilities

• Autorzy: Zhernovyi Yuriy , Kopytko Bohdan

Identyfikatory

DOI

10.17512/jamcm.2020.3.10

• Języki publikacji: EN

Abstrakty

EN

In this paper, we propose a method for studying the reliability of series systems with redundancy and repair facilities. We consider arbitrary distributions of the units’ time to failure and exponentially distributed recovery times. The approach based on the use of fictitious phases and hyperexponential approximations of arbitrary distributions by the method of moments. We consider cases of fictitious hyperexponential distributions with paradoxical and complex parameters. We define conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best and same accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.

Słowa kluczowe

EN

reliability; recoverable system; redundancy; series system; hyperexponential approximation; fictitious phases; method of moments

PL

niezawodność; redundancja; system szeregowy; metoda momentów

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 3
• Strony: 123--131
• Opis fizyczny: Bibliogr. 11 poz., tab.

Twórcy

autor

Zhernovyi Yuriy

• Ivan Franko National University of Lviv, Lviv, Ukraine

autor

Kopytko Bohdan

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

• [1] Ushakov, I. (2012). Probabilistic Reliability Models. Hoboken: John Wiley & Sons.
• [2] Zhernovyi, Yu., & Kopytko, B. (2020). Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation. J. Appl. Math. Comput. Mech., 19(1), 113-120.
• [3] Zhernovyi, Yu.V., & Zhernovyi, K.Yu. (2015). Method of potentials for a closed system with queue length dependent service times. J. of Communications Technology and Electronics, 60(12), 1341-1347.
• [4] Aliyev, S.A., Yeleyko, Y.I., & Zhernovyi, Yu.V. (2019). Calculating steady-state probabilities of closed queueing systems using hyperexponential approximation. Caspian J. of Appl. Math., Economics and Ecology, 7(1), 46-55.
• [5] Ryzhikov, Yu.I., & Ulanov, A.V. (2016). Application of hyperexponential approximation in the problems of calculating non-Markovian queuing systems. Vestnik of Tomsk State University. Management, Computer Engineering and Informatics, 3(36), 60-65 (in Russian).
• [6] Zhernovyi, Yu.V. (2018). Calculating steady-state characteristics of single-channel queuing systems using phase-type distributions. Cybernetics and Systems Analysis, 54(5), 824-832.
• [7] Zhernovyi, Yu. & Kopytko, B. (2019). Calculating steady-state probabilities of queueing systems using hyperexponential approximation. J. Appl. Math. Comput. Mech., 18(2), 111-122.
• [8] Zhernovyi, Yu. (2019). Computing Non-Markovian Queues Using Hyperexponential Distributions. Riga: LAP Lambert Academic Publishing.
• [9] Zhernovyi, Yu. (2015). Creating Models of Queueing Systems Using GPSS World. Saarbrucken: LAP Lambert Academic Publishing.
• [10] Zhernovyi, Yu. V. (2020). Simulation Models of Reliability. Zhytomyr: PC ”Zhytomyr-Polygraph” (in Ukrainian).
• [11] Konig, D., Rykov, V.V., & Schmidt, F. (1981). Stationary queuing systems with dependencies. Itogi Nauki i Tekhniki. Ser. Probability Theory, Math. Stat. Theor Cybernet. 18, 95-186 (in Russian).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).