Öncelikli Onarım Kuralı Kullanarak Tamir Edilebilir Ardıl n-den-k-çıkışlı:F Sisteminin Stokastik Analizi Üzerine Bir Çalışma

Year 2025, Volume: 30 Issue: 2, 555 - 571, 31.08.2025

Sevcan Demir Atalay , Agah Kozan , Gözde Kuş

https://doi.org/10.53433/yyufbed.1592928

Abstract

Bu makalede, bileşenlerin arıza ve onarım sürelerinin geometrik dağılıma uyduğu varsayımı altında tamir edilebilir ardıl n-den-k-çıkışlı:F sistemi incelenmiştir. Sisteminin güvenilirlik ve kullanılabilirlik özellikleri, kararlı durum olasılıkları yerine geçiş durum olasılıkları değerlendirilerek elde edilmiştir. Ayrıca, bileşenlerin onarımında öncelikli onarım kuralı uygulanmıştır. Teorik sonuçların elde edilmesi ve teorik olarak elde edilen sonuçların karşılaştırılması aşamasında bir simülasyon çalışması gerçekleştirilmiştir. Sisteme dair çıkarımlarda bulunmak amacı ile çeşitli sayısal sonuçlar elde edilmiş ve bu sonuçlar tablo ve şekillerle sunulmuştur.

Keywords

Geometrik dağılım , Kullanılabilirlik , Monte Carlo simülasyonu , Öncelikli onarım kuralı , Tamir edilebilir Ardıl n-en-k-çıkışlı:F sistem

On the Stochastic Analysis of Consecutive-k-out-of-n:F Repairable System Using Higher Priority Repair Rule

Abstract

In this paper, we study a repairable consecutive-k-out-of-n:F system under the assumption that the failure and repair times of the components follow a geometric distribution. The reliability and availability characteristics of the system are obtained by evaluating transition state probabilities instead of steady state probabilities. Furthermore, the priority repair rule is applied to repair the components. A simulation study was carried out to compare the theoretical results. In order to make inferences about the system, various numerical results are obtained and these results are presented in tables and figures.

Keywords

Availability , Consecutive-k-out-of-n:F repairable system , Geometric distribution , Monte Carlo simulation , Priority repair rule

References

• Ascher, H., & Feingold, H. (1984). Repairable systems reliability. New York: M. Dekker.
• Barbu, V. S., & Limnios, N. (2008). Reliability of semi-Markov systems in discrete time: Modeling and estimation. In K. B. Misra (Ed), Handbook of performability engineering (pp. 369-380). Springer. https://doi.org/10.1007/978-1-84800-131-2_24
• Barlow, R. E., & Proschan, F. (1965). Mathematical theory of reliability. Wiley-Interscience.
• Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing: Probability models. Holt, Rinehart and Winston.
• Bhattacharya, S. K., & Kumar, S. (1985). Discrete life testing. IAPQR Transactions, 13, 71-76.
• Caballéa, N. C., & Castro, I. T. (2018). Assessment of the maintenance cost and analysis of availability measures in a finite life cycle for a system subject to competing failures. Reliability Engineering & System Safety, 41, 255-290. https://doi.org/10.1007/s00291-018-0521-7
• Chao, M.T., Fu, J.C., & Koutras, M.V. (1995). Survey of reliability studies of consecutive-k-out-of-n:F and related systems. IEEE Transactions on Reliability, 44, 120–127. https://doi.org/10.1109/24.376531
• Cheng, K., & Zhang, Y. L. (2001). Analysis for a consecutive-k-out-of-n:F repairable system with priority in repair. International Journal of Systems Science, 32(5), 591-598. https://doi.org/10.1080/00207720119474
• Chiang, D.T., & Niu, S. (1981). Reliability of consecutive-k-out-of-n:F. IEEE Transactions on Reliability. 30. 87–89. https://doi.org/10.1109/TR.1981.5220981
• Elsayed, E. A. (2012). Reliability engineering. John Wiley & Sons.
• Eryilmaz, S. (2010). Review of recent advances in reliability of consecutive k-out-of-n and related systems. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 224(3), 225-237. https://doi.org/10.1243/1748006XJRR332
• Eryilmaz. S. (2014). Computing reliability indices of repairable systems via signature. Journal of Computational and Applied Mathematics, 260, 229–235. https://doi.org/10.1016/j.cam.2013.09.023
• Eryilmaz, S. (2016). Discrete time cold standby repairable system: Combinatorial analysis. Communications in Statistics-Theory and Methods, 45(24), 7399-7405. https://doi.org/10.1080/03610926.2013.776689
• Eryilmaz, S., & Finkelstein, M. (2021). Reliability of the two-unit priority standby system revisited. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 236(6), 1096-1103. https://doi.org/10.1177/1748006X211051828
• Gao, S., Wang, J., & Chen, Q. (2025). Reliability evaluation for a circular con/k/n:F system with a novel differential repair policy. IEEE Transactions on Reliability, https://doi.org/10.1109/TR.2024.3524329
• Gökdere, G., & Tony Ng, H. K. (2021). Time-dependent reliability analysis for repairable consecutive-k-out-of-n:F system. Statistical Theory and Related Fields. 6(2). 139–147. https://doi.org/10.1080/24754269.2021.1971489
• Guan, J., & Wu, Y. (2006). Repairable consecutive-k-out-of-n:F system with fuzzy states. Fuzzy Sets and Systems, 157, 121-142. https://doi.org/10.1016/j.fss.2005.05.025
• Gupta, R., & Bhardwaj, P. (2019). A discrete parametric Markov-chain model of a two unit cold standby system with appearance and disappearance of repairman. Reliability: Theory & Applications, 14(1), 13-22. https://doi.org/10.24411/1932-2321-2019-11002
• Kontoleon, J. M. (1980). Reliability determination of a r-successive-out-of-n:F system. IEEE Transactions on Reliability, 29, 437-437. https://doi.org/10.1109/TR.1980.5220921
• Kumar, U. D., & Gopalan, M. N. (1997). Analysis of consecutive k-out-of-n:F systems with single repair facility. Microelectronics Reliability. 37(4). 587–590. https://doi.org/10.1016/S0026-2714(96)00089-3
• Lam, Y., & Ng, H. K. T. (2001). A general model for consecutive-k-out-of-n:F repairable system with exponential distribution and (k-1)-step Markov dependence. European Journal of Operational Research, 129, 663-682. https://doi.org/10.1016/S0377-2217(99)00474-9
• Li, M., Hu, L., Peng, R., & Bai, Z. (2021). Reliability modeling for repairable circular consecutive-k-out-of-n: F systems with retrial feature. Reliability Engineering & System Safety, 216, 107957. https://doi.org/10.1016/j.ress.2021.107957
• Lisnianski, A., Frenkel, I., & Ding, Y. (2010). Modern stochastic process methods for multi-state system reliability assessment. In Multi-State system reliability analysis and optimization for engineers and industrial managers (pp. 29–115). Springer, London.
• Liu, Y., Qu, Z., Li, X., An, Y., & Yin, W. (2019). Reliability modeling for repairable systems with stochastic lifetimes and uncertain repair times. IEEE Transactions on Fuzzy Systems, 27(12), 2396-2405. https://doi.org/10.1109/TFUZZ.2019.2898617
• Maiti, S. S., & Murmu, S. (2015). Bayesian estimation of reliability in two-parameter geometric distribution. Journal of Reliability and Statistical Studies, 41-58.
• Mehdi, I., Boudi, E. M., & Mehdi, M. A. (2024). Reliability, availability, and maintainability assessment of a mechatronic system based on timed colored Petri nets. Applied Sciences, 14(11), 4852. https://doi.org/10.3390/app14114852
• Mirzaei, D., Behbahaninia, A., Abdalisousan, A., & Miri Lavasani, S. M. (2023). Annual availability assessment of a gas turbine power plant using Monte Carlo simulation based on fuzzy logic and an adaptive neuro-fuzzy repair time prediction system. Journal of Thermal Analysis and Calorimetry, 148(16), 8675-8696. https://doi.org/10.1007/s10973-023-12091-7
• Oszczypała, M., Konwerski, J., Ziółkowski, J., & Małachowski, J. (2024). Reliability analysis and redundancy optimization of k-out-of-n systems with random variable k using continuous time Markov chain and Monte Carlo simulation. Reliability Engineering & System Safety. 242, 109780. https://doi.org/10.1016/j.ress.2023.109780
• Srinivasa Rao, M., & Naikan, V. N. A. (2014). Reliability analysis of repairable systems using system dynamics modeling and simulation. Journal of Industrial Engineering International, 10(69). https://doi.org/10.1007/s40092-014-0069-3
• Villén-Altamirano, J. (2010). RESTART simulation of non-Markov consecutive k-out-of-n:F repairable systems. Reliability Engineering & System Safety, 95, 247-254. https://doi.org/10.1016/j.ress.2009.10.005
• Wu, Y., & Guan, J. (2005). Repairable consecutive-k-out-of-n:G systems with r repairmen. IEEE Transactions on Reliability. 54(2). 328-337. https://doi.org/10.1109/TR.2005.847250
• Xiao, G., Li, Z., & Li, T. (2007). Dependability estimation for non-Markov consecutive k-out-of-n:F repairable systems by fast simulation. Reliability Engineering & System Safety, 92(3), 293-299. https://doi.org/10.1016/j.ress.2006.04.004
• Yaqub, M., & Khan, A. H. (1981). Geometric failure law in life testing. Pure and Applied Mathematika Science, 14(1-2), 69-76.
• Yam, R. C. M., Zuo, M. J., & Zhang, Y. L. (2003). A method for evaluation of reliability indices for repairable circular consecutive-k-out-of-n:F systems. Reliability Engineering & System Safety, 79, 1–9. https://doi.org/10.1016/S0951-8320(02)00204-1
• Yang, D-Y, Wu, Z-R, & Tsou, C-S. (2014). Reliability analysis of a repairable system with geometric reneging and threshold-based recovery policy. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 229(11), 2047-2062. https://doi.org/10.1177/0954405414540649
• Zhang, Y. L., & Wang, T. P. (1996). Repairable consecutive-2-out-of-n:F system. Microelectronics Reliability, 36(5), 605-608. https://doi.org/10.1016/0026-2714(95)00183-2
• Zhang, C., Yang, J., Li, M., & Wang, N. (2024). Reliability analysis of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system. Reliability Engineering & System Safety, 242, 109792. https://doi.org/10.1016/j.ress.2023.109792