A combined method for reliability analysis of multi-state system of minor-repairable components

• Autorzy: Qin J. , Niu Y. , Li Z.

Identyfikatory

DOI

10.17531/ein.2016.1.11

Warianty tytułu

PL

Łączona metoda analizy niezawodności systemu wielostanowego skła dającego się z elementów podlegających drobnej naprawie

• Języki publikacji: EN

Abstrakty

EN

This paper discusses the multi-state system (MSS) consisted of multi-state components with minor failure and minor repair. In order to obtain the reliability indices of MSS, a new combined method is suggested. This method is based on the Markov stochastic process and the universal generating function (UGF) technology. The traditional idea of modeling the MSS is to use straightforward Markov process. That is not effective enough for the MSS because the model of the system is complicated usually and the state space often arouses “dimension curse” - huge numbers of the states. We suggest it should model the multi-state components and the UGF of multi-state components can be obtained firstly. Then the MSS can be decomposed into several subsystems which only contain simple series-parallel structure. According to the physical nature of the subsystems, the UGF of those subsystems can be employed recursively. Furthermore the UGF of the entire MSS will be obtained. Therefore, the reliability indices of the MSS can be evaluated easily. The suggested method simplifies greatly the complexity of calculation and is well formulized. Two numerical examples illustrate this method.

PL

W artykule omówiono system wielostanowy (multi-state system, MSS) składający się z elementów wielostanowych, które mogą ulegać drobnym uszkodzeniom i podlegają drobnym naprawom. Zaproponowano nową metodę łączoną, która pozwala wyznaczać wskaźniki niezawodności MSS. Metoda ta opiera się na procesie stochastycznym Markowa oraz technologii uniwersalnej funkcji tworzącej (universal generating function, UGF). Tradycyjnie do modelowania MSS wykorzystuje się sam proces Markowa. Metoda ta nie jest jednak wystarczająco skuteczna w przypadku MSS, ponieważ modele tego typu systemów są zazwyczaj skomplikowane, a przestrzeń stanów często prowadzi do tzw. "przekleństwa wielowymiarowości" – konieczności uwzględnienia ogromnej liczby stanów. Nasza metoda polega na modelowaniu elementów wielostanowych, dla których, w pierwszej kolejności wyznacza się UGF. Następnie MSS można rozłożyć na kilka podsystemów, które mają prostą strukturę szeregowo-równoległą. Charakter fizyczny tych podsystemów, pozwala na rekurencyjne stosowanie UGF dla tych podsystemów. Ponadto metoda umożliwia wyznaczenie UGF dla całego MSS, co pozwala na łatwą ocenę wskaźników niezawodności MSS. Proponowana metoda znacznie upraszcza obliczenia i jest dobrze sformalizowana. W pracy przedstawiono dwa przykłady numeryczne, które ilustrują omawianą metodę.

Słowa kluczowe

EN

multi-state system; reliability index; Markov stochastic process; universal generating function; minor repair

PL

system wielostanowy; wskaźnik niezawodności; proces stochastyczny Markowa; uniwersalna funkcja tworząca; drobne naprawy

• Wydawca: Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne
• Czasopismo: Eksploatacja i Niezawodność
• Rocznik: 2016
• Tom: Vol. 18, no. 1
• Strony: 80--88
• Opis fizyczny: Bibliogr. 45 poz., rys., tab.

Twórcy

autor

Qin J.

• Information and Network Management Center North China Electric Power University Baoding, 071003, China

autor

Niu Y.

• State Key Laboratory of Alternate Electric Power System with Renewable Energy Sources North China Electric Power University Beijing, 102206, China

autor

Li Z.

• Department of Computer Science and Technology North China Electric Power University Baoding, 071003, China

Bibliografia

• 1. Anatoly, L. and F. Ilia. Recent Advances in System Reliability. London, Springer-Verlag, 2012.
• 2. Anatoly Lisnianski, D. E., David Laredo, Hanoch Ben Haim. A multi-state Markov model for a short-term reliability analysis of a power generating unit. Reliability Engineering and System Safety 2012; 98(1): 1-6, http://dx.doi.org/10.1016/j.ress.2011.10.008.
• 3. Aven, T. and U. Jensen. Stochastic Models in Reliability. New York, Springer-Verlag, 1999. http://dx.doi.org/10.1007/b97596
• 4. Barlow, R. E. Mathematical reliability theory: from the beginning to the present time 2002; World Scientific.
• 5. Barlow, R. E. Mathematical theory of reliability: A historical perspective. Reliability, IEEE Transactions on 1984; R-33(1): 16-20, http://dx.doi.org/10.1109/tr.1984.6448269.
• 6. Barlow, R. E. and F. Proschan. Mathematical theory of reliability. New York, Wiley, 1965.
• 7. Barlow, R. E. and A. S. Wu. Coherent Systems with Multi-State Components. Mathematics of Operations Research 1978; 3(4): 275-281. http://dx.doi.org/10.1287/moor.3.4.275
• 8. Chang, P. C. and Y. K. Lin. Fuzzy-based system reliability of a labour-intensive manufacturing network with repair. International Journal of Production Research 2015; 53(7): 1980-1995, http://dx.doi.org/10.1080/00207543.2014.944279.
• 9. Di Maio, F., D. Colli, E. Zio, L. Tao and J. Tong. A Multi-State Physics Modeling approach for the reliability assessment of Nuclear Power Plants piping systems. Annals of Nuclear Energy 2015; 80: 151-165, http://dx.doi.org/10.1016/j.anucene.2015.02.007.
• 10. Ding, Y. and A. Lisnianski. Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets and Systems 2008; 159(3): 307-324, http://dx.doi.org/10.1016/j.fss.2007.06.004.
• 11. Doostparast, M., F. Kolahan and M. Doostparast. A reliability-based approach to optimize preventive maintenance scheduling for coherent systems. Reliability Engineering & System Safety 2014; 126(0): 98-106, http://dx.doi.org/10.1016/j.ress.2014.01.010.
• 12. Gandini, A. Importance and sensitivity analysis in assessing system reliability. Reliability, IEEE Transactions on 1990; 39(1): 61-70, http://dx.doi.org/10.1109/24.52613.
• 13. Guilani, P. P., M. Sharifi, S. T. A. Niaki and A. Zaretalab. Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods. Reliability Engineering & System Safety 2014; 129: 29-35, http://dx.doi.org/10.1016/j.ress.2014.04.019.
• 14. Janan, X. On Multistate System Analysis. Reliability, IEEE Transactions on 1985; R-34(4): 329-337.
• 15. Levitin, G. Block diagram method for analyzing multi-state systems with uncovered failures. Reliability Engineering & System Safety 2007; 92(6): 727-734, http://dx.doi.org/10.1016/j.ress.2006.02.009.
• 16. Levitin, G. The universal generating function in reliability analysis and optimization. London, Springer-Verlag, 2005.
• 17. Levitin, G. and A. Lisnianski. Joint redundancy and maintenance optimization for multistate series-parallel systems. Reliability Engineering & System Safety 1999; 64(1): 33-42, http://dx.doi.org/10.1016/S0951-8320(98)00052-0.
• 18. Levitin, G., A. Lisnianski, H. Ben-Haim and D. Elmakis. Redundancy optimization for series-parallel multi-state systems. Reliability, IEEE Transactions on 1998; 47(2): 165-172, http://dx.doi.org/10.1109/24.722283.
• 19. Levitin, G., L. Xing, H. Ben-Haim and Y. Dai. Multi-state systems with selective propagated failures and imperfect individual and group protections. Reliability Engineering & System Safety 2011; 96(12): 1657-1666, http://dx.doi.org/10.1016/j.ress.2011.08.002.
• 20. Levitin, G., L. Xing, H. Ben-Haim and Y. Dai. Reliability of Series-Parallel Systems With Random Failure Propagation Time. Ieee Transactions on Reliability 2013; 62(3): 637-647, http://dx.doi.org/10.1109/TR.2013.2270415.
• 21. Li, C.-y., X. Chen, X.-s. Yi and J.-y. Tao. Heterogeneous redundancy optimization for multi-state series-parallel systems subject to common cause failures. Reliability Engineering & System Safety 2010; 95(3): 202-207, http://dx.doi.org/10.1016/j.ress.2009.09.011.
• 22. Li, W. and M. J. Zuo. Reliability evaluation of multi-state weighted k-out-of-n systems. Reliability Engineering & System Safety 2008; 93(1): 160-167, http://dx.doi.org/10.1016/j.ress.2006.11.009.
• 23. Lin, Y.-K. and C.-F. Huang. Reliability Evaluation of a Multi-state Network with Multiple Sinks under Individual Accuracy Rate Constraint. Communications in Statistics-Theory and Methods 2014; 43(21): 4519-4533, http://dx.doi.org/10.1080/03610926.2012.716137.
• 24. Lisnianski, A. and Y. Ding. Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique. Reliability Engineering & System Safety 2009; 94(11): 1788-1795, http://dx.doi.org/10.1016/j.ress.2009.05.006.
• 25. Lisnianski, A., G. Levitin and H. Ben-Haim. Structure optimization of multi-state system with time redundancy. Reliability Engineering & System Safety 2000; 67(2): 103-112, http://dx.doi.org/10.1016/S0951-8320(99)00049-6.
• 26. Ming Tan, C. and N. Raghavan. A framework to practical predictive maintenance modeling for multi-state systems. Reliability Engineering & System Safety 2008; 93(8): 1138-1150, http://dx.doi.org/10.1016/j.ress.2007.09.003.
• 27. Mo, Y. C., L. D. Xing, S. V. Amari and J. B. Dugan. Efficient analysis of multi-state k-out-of-n systems. Reliability Engineering & System Safety 2015; 133: 95-105, http://dx.doi.org/10.1016/j.ress.2014.09.006.
• 28. Nahas, N., A. Khatab, D. Ait-Kadi and M. Nourelfath. Extended great deluge algorithm for the imperfect preventive maintenance optimization of multi-state systems. Reliability Engineering & System Safety 2008; 93(11): 1658-1672, http://dx.doi.org/10.1016/j.ress.2008.01.006.
• 29. Nourelfath, M. and D. Ait-Kadi. Optimization of series-parallel multi-state systems under maintenance policies. Reliability Engineering & System Safety 2007; 92(12): 1620-1626, http://dx.doi.org/10.1016/j.ress.2006.09.016.
• 30. Pandey, M., M. J. Zuo and R. Moghaddass. Selective maintenance modeling for a multistate system with multistate components under imperfect maintenance. IIE Transactions 2013; 45(11): 1221-1234, http://dx.doi.org/10.1080/0740817X.2012.761371.
• 31. Parikh, C. R., M. J. Pont and N. Barrie Jones. Application of Dempster¨CShafer theory in condition monitoring applications: a case study. Pattern Recognition Letters 2001; 22(6): 777-785, http://dx.doi.org/10.1016/S0167-8655(01)00014-9.
• 32. Rami, A., H. Hamdaoui, H. Sayah and A. Zeblah. Efficient harmony search optimization for preventive-maintenance-planning for nuclear power systems. International Journal for Simulation and Multidisciplinary Design Optimization 2014; 5: A17, http://dx.doi.org/10.1051/smdo/2013011.
• 33. Rueda, A. and M. Pawlak. Pioneers of the reliability theories of the past 50 years. Reliability and Maintainability, 2004 Annual Symposium - RAMS 2004; 102-109, http://dx.doi.org/10.1109/rams.2004.1285431.
• 34. Tian, Z., G. Levitin and M. J. Zuo. A joint reliability-redundancy optimization approach for multi-state series-parallel systems. Reliability Engineering & System Safety 2009; 94(10): 1568-1576, http://dx.doi.org/10.1016/j.ress.2009.02.021.
• 35. Ushakov. "Reliability: past, present, future," Recent Advances in Reliability Theory: Methodology, Practice, and Interface,. Boston, Birkhäuser, 2000.
• 36. Ushakov, I. Optimal standby problems and a universal generating function. Soviet journal of computer and systems sciences 1987; 25(4): 79-82.
• 37. Wang, L., X. Jia and J. Zhang. Reliability Evaluation for Multi-State Markov Repairable Systems with Redundant Dependencies. Quality Technology and Quantitative Management 2013; 10(3): 277-289.
• 38. Xiao, H. and R. Peng. Optimal allocation and maintenance of multi-state elements in series-parallel systems with common bus performance sharing. Computers & Industrial Engineering 2014; 72(0): 143-151, http://dx.doi.org/10.1016/j.cie.2014.03.014.
• 39. Yeh, W.-C. Evaluation of all one-to-many reliabilities for acyclic multistate-node distributed computing system under cost and capacity constraints. Computer Communications 2007; 30(18): 3796-3806, http://dx.doi.org/10.1016/j.comcom.2007.09.005.
• 40. Yeh, W. C. A novel node-based sequential implicit enumeration method for finding all d-MPs in a multistate flow network. Information Sciences 2015; 297: 283-292, http://dx.doi.org/10.1016/j.ins.2014.11.007.
• 41. Yu, L. and H. Hong-Zhong. Optimal Selective Maintenance Strategy for Multi-State Systems Under Imperfect Maintenance. Reliability, IEEE Transactions on 2010; 59(2): 356-367, http://dx.doi.org/10.1109/TR.2010.2046798.
• 42. Yu, L. and H. Hong-Zhong. Optimization of multi-state elements replacement policy for multi-state systems. Reliability and Maintainability Symposium (RAMS), 2010 Proceedings - Annual 2010; 1-7.
• 43. Zhou, Y., T. R. Lin, Y. Sun, Y. Bian and L. Ma. An effective approach to reducing strategy space for maintenance optimisation of multistate series-parallel systems. Reliability Engineering & System Safety 2015; 138(0): 40-53, http://dx.doi.org/10.1016/j.ress.2015.01.018.
• 44. Zio, E. Reliability engineering: Old problems and new challenges. Reliability Engineering & System Safety 2009; 94(2): 125-141, http://dx.doi.org/10.1016/j.ress.2008.06.002.
• 45. Zio, E., M. Marella and L. Podofillini. A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies. Reliability Engineering & System Safety 2007; 92(7): 871-882, http://dx.doi.org/10.1016/j.ress.2006.04.024.