Markov reliability models of series systems with redundancy and repair facilities

• Autorzy: Zhernovyi Yuriy , Kopytko Bohdan

Identyfikatory

DOI

10.17512/jamcm.2021.3.08

• Języki publikacji: EN

Abstrakty

EN

In this paper, we use Markov models for studying the reliability of series systems with redundancy and repair facilities. We suppose that the units’ time to failure and recovery times are exponentially distributed. We consider the cases when 1≤ c ≤ m and m + 1 ≤ c ≤ m + n, for the system of n operating units, m unloaded redundant units and c repair facilities. Using the exponential distributions properties, we obtain stationary reliability indices of the series systems: steady-state probabilities, a stationary availability coefficient, mean time to failure, mean time between failures and mean downtime.

Słowa kluczowe

EN

reliability; recoverable system; redundancy; series system; Markov models; mean time to failure; mean time between failures; mean downtime

PL

niezawodność; redundancja; modele Markova; średni czas bezawaryjnej pracy; średni czas pomiędzy uszkodzeniami

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2021
• Tom: Vol. 20, nr 3
• Strony: 89--96
• Opis fizyczny: Bibliogr. 5 poz.

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). Reliability assessment of a series system with redundancy and repair facilities. J. Appl. Math. Comput. Mech., 19(3), 123-131.
• [3] 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.
• [4] 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.
• [5] 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.