Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy Lz -transform

Hu, L.; Zhang, Z.; SU, P.; Peng, R.

doi:10.17531/ein.2017.2.5

Artykuł - szczegóły

Tytuł artykułu

Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy Lz -transform

Autorzy

Hu L. , Zhang Z. , SU P. , Peng R.

Treść / Zawartość

Pełne teksty:

Pobierz

Identyfikatory

DOI

10.17531/ein.2017.2.5

Warianty tytułu

Wykorzystanie rozmytej transformaty do oceny rozmytej gotowości eksploatacyjnej dyskretnego w czasie systemu wielostanowego działającego w trybie drobnych uszkodzeń i napraw

Języki publikacji

Abstrakty

This paper studies assessment approach of dynamic fuzzy availability for a discrete time multi-state system under minor failures and repairs. Traditionally, it was assumed that the exact reliability data of a component/system with discrete time are given in reliability analysis. In practical engineering, it is difficult to obtain precise data to evaluate the characteristics of a component/system. To overcome the problem, fuzzy set theory is employed to deal with dynamic availability assessment for a discrete time multi-state system in this paper. A fuzzy discrete time Markov model with fuzzy transition probability matrix is proposed to analyze the fuzzy state probability of each component at any discrete time. The fuzzy Lz-transform of the discrete-state discrete-time fuzzy Markov chain is developed to extend the Lz-transform of the discrete-state continuous-time Markov model with crisp sets. Based on the α-cut approach and the fuzzy Lz-transform, the dynamic fuzzy availability of the system is computed by using parametric programming technique. To illustrate the proposed method, a flow transmission system is analyzed as a numerical example.

W niniejszej pracy badano metodę oceny dynamicznej, rozmytej gotowości eksploatacyjnej (dostępności) dyskretnego w czasie systemu wielostanowego pracującego w trybie drobnych uszkodzeń i napraw. Tradycyjnie zwykło się zakładać, że analiza niezawodności dostarcza dokładnych danych niezawodnościowych na temat danego dyskretnego w czasie komponentu/systemu. W praktyce inżynieryjnej jednak trudno jest uzyskać dokładne dane do oceny właściwości komponentu/systemu. W niniejszej pracy zaproponowano jak problem ten można rozwiązać wykorzystując do oceny dynamicznej gotowości dyskretnego w czasie systemu wielostanowego, teorię zbiorów rozmytych. Rozmyty model Markowa z dyskretnym czasem i rozmytą macierzą prawdopodobieństw przejść zastosowano do analizy rozmytego prawdopodobieństwa stanu każdego elementu w dowolnym czasie dyskretnym. Opracowano rozmytą transformatę Lz rozmytego, dyskretnego w stanach i czasie łańcucha Markowa, która pozwala poszerzyć transformatę Lz modelu Markowa dyskretnego w stanach i ciągłego w czasie o zbiory ostre. W oparciu o metodę alfa przekrojów oraz rozmytą transformatę Lz, obliczono dynamiczną rozmytą gotowość eksploatacyjną systemu, wykorzystując do tego celu technikę programowania parametrycznego. Zastosowanie proponowanej metody zilustrowano na przykładzie liczbowym analizując układ przesyłu.

Słowa kluczowe

discrete time Markov model fuzzy Lz-transform Multi-State System availability

czas dyskretny model Markova rozmyta transformata system wielostanowy dostępność

Wydawca

Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne

Czasopismo

Eksploatacja i Niezawodność

Rocznik

2017

Tom

Vol. 19, no. 2

Strony

179--190

Opis fizyczny

Bibliogr. 42 poz., rys., tab.

Twórcy

autor

Hu L.

linminhu@ysu.edu.cn

College of Science Yanshan University Qinhuangdao 066004, P. R. China

autor

Zhang Z.

College of Science Yanshan University Qinhuangdao 066004, P. R. China

autor

SU P.

College of Science Yanshan University Qinhuangdao 066004, P. R. China

autor

Peng R.

pengrui1988@ustb.edu.cn

Donlinks School of Economics & Management University of Science & Technology Beijing Beijing 100083, P. R. China

Bibliografia

1. Amico G. Single-use reliability computation of a semi-Markovian system. Applications of Mathematics 2014; 59(5): 571-588, https://doi.org/10.1007/s10492-014-0072-4.
2. Backley J. Fuzzy Probabilities: New Approach and Applications. Springer, 2005.
3. Bamrungsetthapong W, Pongpullponsak A. System reliability for non-repairable multi-state series–parallel system using fuzzy Bayesian inference based on prior interval probabilities. International Journal of General Systems 2015; 44(4): 442-456, https://doi.org/10.1080/03081079.2014.976215.
4. Barbu V, Limnios N. Empirical estimation for discrete time semi-Markov processes with applications in reliability. Journal of Nonparametric Statistics 2006; 18(7-8): 483-498, https://doi.org/10.1080/10485250701261913.
5. Bracquemond C, Gaudoin O. A survey on discrete lifetime distributions. International Journal on Reliability, Quality, and Safety Engineering 2003; 10(1), 69-98, https://doi.org/10.1142/S0218539303001007.
6. Brameret P, Raury A, Roussel J. Automated generation of partial Markov chain form high level descriptions. Reliability Engineering and System Safety 2015; 139: 179-187, https://doi.org/10.1016/j.ress.2015.02.009.
7. Cai K. Introduction to Fuzzy Reliability, Dordrecht: Kluwer Academic Publishers, 1996, https://doi.org/10.1007/978-1-4613-1403-5.
8. Castro H, Cavalca K. Maintenance resourced optimization applied to a manufacturing system. Reliability Engineering and System Safety 2006; 91(4): 413-420, https://doi.org/10.1016/j.ress.2005.02.004.
9. Chen Y L, Chang C C, Sheu D F. Optimum random and age replacement policies for customer demand multi-state system reliability under imperfect maintenance. International Journal of Systems Science 2016; 47(5): 1130-1141, https://doi.org/10.1080/00207721.2014.915353.
10. Chryssaphinou O, Limnios N. Multi-state reliability systems under discrete time semi Markovian hypothesis. IEEE Transactions on Reliability 2011; 60(1): 80-87, https://doi.org/10.1109/TR.2010.2104210.
11. Da Q, Liu X. Interval number linear programming and its satisfactory solution. Systems Engineering Theory and Practice 1999; 19(4): 3-7.
12. Ding Y, Lisnianski A. Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets and Systems 2008; 159(3): 307-324, https://doi.org/10.1016/j.fss.2007.06.004.
13. Ding Y, Zuo M, Lisnianski A, Tian Z. Fuzzy multi-state systems: general definitions, and performance assessment. IEEE Transactions on Reliability 2008; 57(4): 589-594, https://doi.org/10.1109/TR.2008.2006078.
14. Eryilmaz S. On Mean residual life of discrete time multi-state systems. Quality Technology and Quantitative Management 2013; 10(2): 241-249, https://doi.org/10.1080/16843703.2013.11673319.
15. Garg H. An approach for analyzing the reliability of industrial system using fuzzy Kolmogorov's differential equations. Arabian Journal for Science and Engineering 2015; 40: 975 987, https://doi.org/10.1007/s13369-015-1584-2.
16. Guerry M. On the embedding problem for discrete-time Markov chains. Journal of Applied Probability 2013; 50(4): 918-930, https://doi.org/10.1017/S002190020001370X.
17. Hu L, Yue D, Tian R. Fuzzy availability assessment for a repairable multi-state series-parallel system. Discrete Dynamics in Nature and Society 2015; Article ID 156059, https://doi.org/10.1155/2015/156059.
18. Huang H. Structural reliability analysis using fuzzy sets theory. Eksploatacja i Niezawodnosc– Maintenance and Reliability 2012; 14(4): 284-294.
19. Jin Q, Sugasawa Y. Representation and analysis of behavior for multiprocess systems by using stochastic Petri nets. Mathematical and Computer Modelling 1995; 22(10-12): 109-118, https://doi.org/10.1016/0895-7177(95)00187-7.
20. Ke J, Huang H, Lin C. Fuzzy analysis for steady state availability: a mathematical programming approach. Engineering Optimization 2006; 38(8): 909-921, https://doi.org/10.1080/03052150600795854.
21. Kumar G, Jain V, Gandhi O. Reliability and availability modeling of mechanical systems using stochastic Petri Net. Proceedings of the ASME 2011 Power Conference 2011; 211-220, Denver, Colorado, USA, https://doi.org/10.1115/POWER2011-55325.
22. Kumar S, Kumar B, Chaudhary A. Reliability analysis of a discrete life time model. International Journal of Computer Applications 2014; 86(10): 35-39, https://doi.org/10.5120/15024-3313.
23. Kurano M, Yasuda M, Nakagami J, Yoshida Y. A fuzzy approach to Markov decision processes with uncertain transition probabilities. Fuzzy Sets and Systems 2006; 157(19): 2674 2682, https://doi.org/10.1016/j.fss.2004.10.023.
24. Levitin G, Zhang T, Xie M. State probability of a series-parallel repairable system with two types of failure states. International Journal of Systems Science 2006; 37(14): 1011-1020, https://doi.org/10.1080/00207720600903201.
25. Li C, Chen X, Yi X, Tao J. Interval-valued reliability analysis of multi-state systems. IEEE Transactions on Reliability 2011; 60(1): 323-330, https://doi.org/10.1109/TR.2010.2103670.
26. Li G, Xiu B. Fuzzy Markov chains based on the fuzzy transition probability. Chinese Control and Decision Conference 2014; 4351-4356, https://doi.org/10.1109/ccdc.2014.6852945.
27. Li Z, Kapur K C. Continuous-state reliability measures based on fuzzy sets. IIE Transactions 2012; 44: 1033-1044, https://doi.org/10.1080/0740817X.2011.588684.
28. Lisnianski A. Lz-transform for a discrete-state continuous-time Markov process and its application to multi-state system reliability. Multi state Systems and Statistical Inference 2012; 79-96, Springer: London.
29. Lisnianski A, Ben-Haim H. Short-term reliability evaluation for power stations by using Lz transform. Journal of Modern Power Systems and Clean Energy 2013; 1(2): 110-117, https://doi.org/10.1007/s40565-013-0021-3.
30. Lisnianski A, Ding Y. Redundancy analysis for repairable multi-state system by Rusing combined stochastic processes methods and universal generating function technique. Reliability Engineering and System Safety 2009; 94(11): 1788-1795, https://doi.org/10.1016/j.ress.2009.05.006.
31. Lisnianski A, Frenkel I, Khvatskin L. On Birnbaum importance assessment for aging Multi state system under minimal repair by using the Lz-transform method. Reliability Engineering and System Safety 2015; 142: 258-266, https://doi.org/10.1016/j.ress.2015.05.006.
32. Lisnianski A, Levitin G. Multi-State System Reliability Assessment, Optimization, Applications. Singapore: World Scientific, 2003, https://doi.org/10.1142/5221
33. Liu Y, Huang H. Reliability Assessment for fuzzy multi-state systems. International Journal of Systems Science 2010; 41(4): 365-379, https://doi.org/10.1080/00207720903042939.
34. Rocha-Martinez J, Shaked M. A discrete-time model of failure and repair. Applied Stochastic Models and Data Analysis 1995; 11(2): 167-180, https://doi.org/10.1002/asm.3150110207.
35. Sadek A, Limnios N. Asymptotic properties for maximum likelihood estimators for reliability and failure rates of Markov chains. Statistics-Theory and Methods 2002; 31(10): 1837-1861, https://doi.org/10.1081/STA-120014916.
36. Sarhan A, Guess F, Usher J. Estimators for reliability measures in geometric distribution model using dependent masked system life test data. IEEE Transactions on Reliability 2007; 56(2): 312-320, https://doi.org/10.1109/TR.2007.895300.
37. Shen J, Cui L. Reliability performance for dynamic systems with cycles of K regimes. IIE Transactions 2016; 48(4): 389-402, https://doi.org/10.1080/0740817X.2015.1110266.
38. Utkin L, Gurov S. A general formal approach for fuzzy reliability analysis in the possibility context. Fuzzy Sets and Systems 1996; 83(2): 203-213, https://doi.org/10.1016/0165 0114(95)00391-6.
39. Zadeh L. Fuzzy sets. Information Control 1965; 8: 338-353, https://doi.org/10.1016/S0019 9958(65)90241-X.
40. Zadeh L. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1978; 1(1): 3-28, https://doi.org/10.1016/0165-0114(78)90029-5.
41. Zio E, Baraldi P, Patelli E. Assessment of the availability of an offshore installation by Monte Carlo simulation. International Journal of Pressure Vessels and Piping 2006; 83(4): 312-320, https://doi.org/10.1016/j.ijpvp.2006.02.010.
42. Zio E, Marella M, Podofillini L. A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies. Reliability Engineering and System Safety 2007; 92(7): 871-882, https://doi.org/10.1016/j.ress.2006.04.024

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-ed240bfb-d30b-4111-a3bf-9d5b0bf41ffd