Abstract
With the increasing complexity and larger size of modern advanced engineering systems, the traditional reliability theory cannot characterize and quantify the complex characteristics of complex systems, such as multi-state properties, epistemic uncertainties, common cause failures (CCFs), etc. This chapter focuses on the reliability analysis of complex multi-state system (MSS) with epistemic uncertainty and CCFs. Based on the Bayesian network (BN) method for reliability analysis of MSS, the DS evidence theory is used to express the epistemic uncertainty in system through the state space reconstruction of MSS. An uncertain state, which used to express the epistemic uncertainty is introduced in the new state space. The integration of evidence theory with BN is achieved by updating the conditional probability tables. When the multiple CCF groups (CCFGs) are considered in complex redundant systems, a modified factor parametric model is introduced to model the CCF in systems. An evidence theory based BN method is proposed for the reliability analysis and evaluation of complex MSSs in this chapter. The reliability analysis of servo feeding control system for CNC heavy-duty horizontal lathes (HDHLs) by this proposed method has shown that the presented method has high computational efficiency and strong practical value.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Gu YK, Li J (2012) Multi-state system reliability: a new and systematic review. Proc Eng 29:531–536
Kančev D, Čepin M (2012) A new method for explicit modelling of single failure event within different common cause failure groups. Reliab Eng Syst Saf 103:84–93
Kohlas J, Monney PA (2013) A mathematical theory of hints: an approach to the Dempster-Shafer theory of evidence. Springer Science & Business Media
Levitin G (2005) The universal generating function in reliability analysis and optimization. Springer, Berlin
Li YF, Zio E (2012) A multi-state model for the reliability assessment of a distributed generation system via universal generating function. Reliab Eng Syst Saf 106:28–36
Lisnianski A, Elmakias D, Laredo D, Ben Haim H (2012) A multi-state Markov model for a short-term reliability analysis of a power generating unit. Reliab Eng Syst Saf 98(1):1–6
Liu YW, Kapur KC (2006) Reliability measures for dynamic multi-state nonrepairable systems and their applications to system performance evaluation. IIE Trans 38(6):511–520
Lorini E, Prade H (2012) Strong possibility and weak necessity as a basis for a logic of desires. In: Working chapters of the ECAI workshop on weighted logics for artificial intelligence, Montpellier, France, pp 99–103
Massim Y, Zeblah A, Benguediab M, Ghouraf A, Meziane R (2006) Reliability evaluation of electrical power systems including multi-state considerations. Electr Eng 88(2):109–116
Mehl CH (2013) P-Boxes for cost uncertainty analysis. Mech Syst Signal Process 37(1–2):253–263
Mi J, Li YF, Huang HZ, Liu Y, Zhang X (2013) Reliability analysis of multi-state systems with common cause failure based on Bayesian networks. Eksploatacja i Niezawodnosc—Maint Reliab 15(2):169–175
Mi J, Li YF, Peng W, Yang Y, Huang HZ (2016) Fault tree analysis of feeding control system for computer numerical control heavy-duty horizontal lathes with multiple common cause failure groups. J Shanghai Jiaotong Univ (Science) 21(4):504–508
Mula J, Poler R, Garcia-Sabater JP (2007) Material requirement planning with fuzzy constraints and fuzzy coefficients. Fuzzy Set Syst 158(7):783–793
Ramirez-Marquez JE, Coit DV (2005) Composite importance measures for multi-state systems with multi-state components. IEEE Trans Reliab 54(3):517–529
Rausand M (2011) Common-Cause Failures. Risk assessment. Wiley, Hoboken, NJ, pp 469–495
Sallak M, Schön W, Aguirre F (2013) Reliability assessment for multi-state systems under uncertainties based on the Dempster-Shafer theory. IIE Trans 45(9):995–1007
Sankararaman S, Mahadevan S (2011) Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data. Reliab Eng Syst Saf 96(7):814–824
Shah H, Hosder S, Winter T (2015) Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions. Reliab Eng Syst Saf 138:59–72
Simon C, Weber P (2009) Evidential networks for reliability analysis and performance evaluation of systems with imprecise knowledge. IEEE Trans Reliab 58(1):69–87
Simon C, Weber P, Levrat E (2007) Bayesian networks and evidence theory to model complex systems reliability. J Comput 2(1):33–43
Simon C, Weber P, Evsukoff A (2008) Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis. Reliab Eng Syst Saf 93(7):950–963
Soundappan P, Nikolaidis E, Haftka RT, Grandhi R, Canfield R (2004) Comparison of evidence theory and Bayesian theory for uncertainty modeling. Reliab Eng Syst Saf 85(1):295–311
Troffaes MCM, Walter G, Kelly D (2014) A robust Bayesian approach to modeling epistemic uncertainty in common-cause failure models. Reliab Eng Syst Saf 125:13–21
Xue J (1985) On multistate system analysis. IEEE Trans Reliab 34(4):329–337
Yang JP, Huang HZ, Liu Y, Li YF (2015) Quantification classification algorithm of multiple sources of evidence. Int J Inf Tech Decis 14(5):1017–1034
Yang X, Liu Y, Zhang Y, Yue Z (2015) Hybrid reliability analysis with both random and probability-box variables. Acta Mech 226(5):1341–1357
Zhang Z, Jiang C, Wang GG, Han X (2015) First and second order approximate reliability analysis methods using evidence theory. Reliab Eng Syst Saf 137:40–49
Zhao S, Wang H, Cheng D (2010) Power distribution system reliability evaluation by DS evidence inference and Bayesian network method. In: IEEE 11th international conference on probabilistic methods applied to power systems pp 654–658
Zhou J, Liu L, Guo J, Sun L (2013) Multisensory data fusion for water quality evaluation using Dempster-Shafer evidence theory. Int J Distrib Sens 1–6
Zhou Q, Zhou H, Zhou Q, Yang F, Luo L, Li T (2015) Structural damage detection based on posteriori probability support vector machine and Dempster-Shafer evidence theory. Appl Soft Comput 36:368–374
Zio E, Podofillini L, Levitin G (2004) Estimation of the importance measures of multi-state elements by Monte Carlo simulation. Reliab Eng Syst Saf 86(3):191–204
Acknowledgements
This research was partially supported by the National Science and Technology Major Project of China under the contract number 2013ZX04013-011, and the Open Project of Traction Power State Key Laboratory of Southwest Jiaotong University under the contract number TPL 1410.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Mi, J., Li, YF., Peng, W., Huang, HZ. (2018). Reliability Analysis of Complex Multi-state System with Common Cause Failure Based on DS Evidence Theory and Bayesian Network. In: Lisnianski, A., Frenkel, I., Karagrigoriou, A. (eds) Recent Advances in Multi-state Systems Reliability. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-63423-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-63423-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63422-7
Online ISBN: 978-3-319-63423-4
eBook Packages: EngineeringEngineering (R0)