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ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

Published online by Cambridge University Press:  19 May 2020

Vladimir Rykov,
Dmitry KozyrevOpen the ORCID record for Dmitry Kozyrev[Opens in a new window],
Andrey Filimonov and
Nika IvanovaOpen the ORCID record for Nika Ivanova[Opens in a new window]
Vladimir Rykov
Affiliation:
National University of Oil and Gas ‘Gubkin University’ (Gubkin University), 65 Leninsky Prospekt, Moscow 119991, Russia; Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation E-mail: rykov-vv@rudn.ru
Dmitry Kozyrev
Affiliation:
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation; V.A.Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, Moscow, 117997, Russia E-mail: kozyrev-dv@rudn.ru
Andrey Filimonov
Affiliation:
Russian University of Transport (MIIT), Obraztsova str. 9, Moscow 115994, Russian Federation E-mail: amfilimonov@yandex.ru
Nika Ivanova
Affiliation:
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation; V.A.Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, Moscow 117997, Russia E-mail: nm_ivanova@bk.ru
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Abstract

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The reliability study of k-out-of-n systems is of interest both from theoretical and practical points of view. Applications of such models can be seen in many real-world phenomena, including telecommunication, transmission, transportation, manufacturing, and services. A probabilistic study of a real-world k-out-of-n system often helps to develop an optimal strategy for maintaining high system-level reliability. There are many investigations devoted to the reliability-centric analysis of such systems. We consider a mathematical model of a repairable k-out-of-n system that works until k of its n components have failed. During the system's life cycle, its components are repaired with the help of a single repair facility. It is supposed that the components' lifetimes have an exponential distribution and their repair times have a general distribution. The proposed model is intended to be applied to the description of operation of unmanned rotorcraft high-altitude platforms and to be validated with the help of an experimental prototype. For the considered system, we propose an algorithm for calculation of the reliability function, and for special cases, k = 2 and k = 3, its closed-form representation is given. A numerical investigation is performed for special cases. The obtained results are a first step toward the sensitivity analysis of reliability characteristics of k-out-of-n systems to the shape of the repair time distributions of their components.

Keywords

reliability characteristicsreliability functionrepairable k-out-of-n system

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 4 , October 2021, pp. 885 - 902
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

References

1.Chakravarthy, S.R., Krishnamoorthy, A., & Ushakumari, P.V. (2001). A (k-out-of-n) reliability system with an unreliable server and phase type repairs and services: The (N, T) policy. Journal of Applied Mathematics and Stochastic Analysis 14(4): 361–380.CrossRefGoogle Scholar
2.Cook, J.L. (2018). Reliability analysis of weighted k-out-of-n systems with variable demand. Quality Engineering 30(4): 687–693. doi:10.1080/08982112.2018.1506132CrossRefGoogle Scholar
3.Cox, D. (1955). The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Mathematical Proceedings of the Cambridge Philosophical Society 51(3): 433–441. doi:10.1017/S0305004100030437.CrossRefGoogle Scholar
4.Gao, H., Cui, L., & Yi, H. (2019). Availability analysis of k-out-of-n:F repairable balanced systems with m sectors. Reliability Engineering & System Safety 191: 106572.CrossRefGoogle Scholar
5.Gao, H., Cui, L., & Chen, J. (2019). Reliability modeling for sparsely connected homogeneous multistate consecutive-k-out-of-n:G systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems (Early Access), 1–11. https://doi.org/10.1109/TSMC.2019.2906550.Google Scholar
6.Gertsbakh, I. & Shpungin, Y. (2016). Reliability of heterogeneous ((k, r)-out-of-(n, m)) system. RTA, No. 3(42), vol. 11, September 2016, pp. 8–10.Google Scholar
7.Goliforushani, S., Xie, M., & Balakrishnan, N. (2018). On the mean residual life of a generalized k-out-of-n system. Communications in Statistics – Theory and Methods 47(10): 2362–2372.CrossRefGoogle Scholar
8.Ke, J.C., Hsu, Y.L., Liu, T.H., & Zhang, Z.G. (2013). Computational analysis of machine repair problem with unreliable multi-repairmen. Computers & Operations Research 40: 848–855.CrossRefGoogle Scholar
9.Kozyrev, D.V., Phuong, N.D., Houankpo, H.G.K., & Sokolov, A. (2019). Reliability evaluation of a hexacopter-based flight module of a tethered unmanned high-altitude platform. Communications in Computer and Information Science, 1141 CCIS, pp. 646–656. doi:10.1007/978-3-030-36625-4_52.CrossRefGoogle Scholar
10.Kuo, W. & Zuo, M.J. (2003). Optimal Reliability Modeling: Principles and Applications. New York: Wiley.Google Scholar
11.Li, X., You, Y., & Fang, R. (2016). On weighted k-out-of-n systems with statistically dependent component lifetimes. Probability in the Engineering and Informational Sciences 30(4): 533–546.CrossRefGoogle Scholar
12.Linton, D.G. & Saw, J.G. (1974). Reliability analysis of the k-out-of-n:F system. IEEE Transactions on Reliability R-23: 97–103.CrossRefGoogle Scholar
13.Moustafa, M.S. (2001). Availability of k-out-of-n:G systems with exponential failure and general repairs. Economic Quality Control 16(1): 75–82.CrossRefGoogle Scholar
14.Ometov, A., Kozyrev, D., Rykov, V., Andreev, S., Gaidamaka, Y., & Koucheryavy, Y. (2017). Reliability-centric analysis of offloaded computation in cooperative wearable applications. Wireless Communications and Mobile Computing 2017, Article ID 9625687, 15 pages. doi:10.1155/2017/9625687.CrossRefGoogle Scholar
15.Perelomov, V.N., Myrova, L.O., Aminev, D.A., & Kozyrev, D.V. (2018). Efficiency enhancement of tethered high altitude communication platforms based on their hardware-software unification. In Vishnevskiy, V. & Kozyrev, D. (eds), Distributed Computer and Communication Networks. DCCN 2018. Communications in Computer and Information Science, vol. 919. Cham: Springer Nature, pp. 184–200. doi:10.1007/978-3-319-99447-5_16.Google Scholar
16.Petrovsky, I.G. (1986). On Cauchy problem for a system of partial differential equations. Nauka: Selected Works, pp. 34–97 (in Russian).Google Scholar
17.Radwan, T., Alrawashdeh, M.J., & Ghanem, S. (2019). An efficient formula for generalized multi-state k-out-of-n:G system reliability. IEEE Access 7: 44823–44830.CrossRefGoogle Scholar
18.Rahmani, R.A., Izadi, M., & Khaledi, B.E. (2016). Stochastic comparisons of total capacity of weighted k-out-of-n systems. Statistics & Probability Letters 117: 216–220.CrossRefGoogle Scholar
19.Rozhdestvensky, B.L. & Yanenko, N.N. (1978). Systems of quasi-linear equations. Moscow: Nauka, 688 p. (in Russian).Google Scholar
20.Ruiz-Castro, J.E. (2020). A complex multi-state k-out-of-n:G system with preventive maintenance and loss of units. Reliability Engineering & System Safety 197: 106797.CrossRefGoogle Scholar
21.Rykov, V. (2018). On reliability of renewable systems. In Vonta, I. & Ram, M. (eds.), Reliability engineering. Theory and applications. Boca Raton: CRC Press, pp. 173–196.CrossRefGoogle Scholar
22.Rykov, V. & Kozyrev, D. (2019). On the reliability function of a double redundant system with general repair time distribution. Applied Stochastic Models in Business and Industry 35(2): 191–197. doi:10.1002/asmb.2368.CrossRefGoogle Scholar
23.Sheng, Y. & Ke, H. (2020). Reliability evaluation of uncertain k-out-of-n systems with multiple states. Reliability Engineering & System Safety 195: 106696.CrossRefGoogle Scholar
24.Shepherd, D.K. (2008). k-out-of-n systems. In F, Ruggeri, R. Kenett & F.W. Faltin (eds.), Encyclopedia of statistics in quality and reliability. Chichester, England: Wiley.Google Scholar
25.Trivedi, K.S. (2002). Probability and statistics with reliability, queuing and computer science applications. New York: Wiley.Google Scholar
26.Wang, K.H., Ke, J.B., & Ke, J.C. (2007). Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Computers and Operations Research 34: 835–847.CrossRefGoogle Scholar
27.Wang, K.H., Chen, W.L., & Yang, D.Y. (2009). Optimal management of the machine repair problem with working vacation: Newton's method. Computational and Applied Mathematics 233: 449–458.CrossRefGoogle Scholar
28.Wang, C., Xing, L., Amari, S.V., & Tang, B. (2020). Efficient reliability analysis of dynamic k-out-of-n heterogeneous phased-mission systems. Reliability Engineering & System Safety 193: 106586.CrossRefGoogle Scholar
29.Wu, H. & Li, Y.-F. (2020). Christophe Bérenguer. Optimal inspection and maintenance for a repairable k-out-of-n:G warm standby system. Reliability Engineering & System Safety 193: 106669.CrossRefGoogle Scholar
30.Yuge, T., Maruyama, M, & Yanagi, S. (2016). Reliability of a (k-out-of-n) system with common-cause failures using multivariate exponential distribution. Procedia Computer Science 96: 968–976.CrossRefGoogle Scholar
31.Zhang, Y. (2018). Optimal allocation of active redundancies in weighted k-out-of-n systems. Statistics & Probability Letters 135: 110–117. doi:10.1016/j.spl.2017.12.002.CrossRefGoogle Scholar
32.Zhang, T., Xie, M., & Horigome, M. (2006). Availability and reliability of (k-out-of-(M + N)): Warm standby systems. Reliability Engineering & System Safety 91: 381–387.CrossRefGoogle Scholar
33.Zhang, Y., Ding, W., & Zhao, P. (2018). On total capacity of k-out-of-n systems with random weights. Naval Research Logistics 65(4): 347–359. doi:10.1002/nav.21810.CrossRefGoogle Scholar