Reliability analysis of complex multi-state system with common cause failure based on evidential networks

Abstract With the increasing complexity and 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). This paper 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 Dempster-Shafer (DS) evidence theory is used to express the epistemic uncertainty in system through the state space reconstruction of MSS, and an uncertain state used to express the epistemic uncertainty is introduced in the new state space. The integration of evidence theory with BN which called evidential network (EN) is achieved by adapting and updating the conditional probability tables (CPTs) into conditional mass tables (CMTs). When multiple CCF groups (CCFGs) are considered in complex redundant system, a modified β factor parametric model is introduced to model the CCF in system. An EN method is proposed for the reliability analysis and evaluation of complex MSSs in this paper. The reliability analysis of servo feeding control system for CNC heavy-duty horizontal lathes (HDHLs) by this proposed method has shown that CCFs have considerable impact on system reliability. The presented method has high computational efficiency, and the computational accuracy is also verified.

[1]  Luca Podofillini,et al.  Estimation of the importance measures of multi-state elements by Monte Carlo simulation , 2004, Reliab. Eng. Syst. Saf..

[2]  Weiwen Peng,et al.  Fault tree analysis of feeding control system for computer numerical control heavy-duty horizontal lathes with multiple common cause failure groups , 2016 .

[3]  Xue Han,et al.  First and second order approximate reliability analysis methods using evidence theory , 2015, Reliab. Eng. Syst. Saf..

[4]  J. Kohlas,et al.  A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of Evidence , 1995 .

[5]  Hong-Zhong Huang,et al.  Belief Universal Generating Function Analysis of Multi-State Systems Under Epistemic Uncertainty and Common Cause Failures , 2015, IEEE Transactions on Reliability.

[6]  Enrico Zio,et al.  A multi-state model for the reliability assessment of a distributed generation system via universal generating function , 2012, Reliab. Eng. Syst. Saf..

[7]  Christopher H. Mehl.  P-boxes for cost uncertainty analysis , 2013 .

[8]  Yu Liu,et al.  Quantification Classification Algorithm of Multiple Sources of Evidence , 2015, Int. J. Inf. Technol. Decis. Mak..

[9]  Philippe Weber,et al.  Bayesian Networks and Evidence Theory to Model Complex Systems Reliability , 2007, J. Comput..

[10]  Shuqiang Zhao,et al.  Power distribution system reliability evaluation by D-S evidence inference and Bayesian network method , 2010, 2010 IEEE 11th International Conference on Probabilistic Methods Applied to Power Systems.

[11]  Li Jing,et al.  Multi-State System Reliability: A New and Systematic Review , 2012 .

[12]  Philippe Weber,et al.  Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis , 2008, Reliab. Eng. Syst. Saf..

[13]  Anatoly Lisnianski,et al.  A multi-state Markov model for a short-term reliability analysis of a power generating unit , 2012, Reliab. Eng. Syst. Saf..

[14]  Fan Yang,et al.  Structural damage detection based on posteriori probability support vector machine and Dempster-Shafer evidence theory , 2015, Appl. Soft Comput..

[15]  Serhat Hosder,et al.  Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions , 2014, Reliab. Eng. Syst. Saf..

[16]  Y. F. Li,et al.  System reliability modeling and assessment for solar array drive assembly based on bayesian networks , 2013 .

[17]  Yung Wen Liu,et al.  Reliability measures for dynamic multistate nonrepairable systems and their applications to system performance evaluation , 2006 .

[18]  Gregory Levitin,et al.  The Universal Generating Function in Reliability Analysis and Optimization , 2005 .

[19]  Raul Poler Escoto,et al.  Material Requirement Planning with fuzzy constraints and fuzzy coefficients , 2007, Fuzzy Sets Syst..

[20]  Xue Janan,et al.  On Multistate System Analysis , 1985, IEEE Transactions on Reliability.

[21]  Sankaran Mahadevan,et al.  Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data , 2011, Reliab. Eng. Syst. Saf..

[22]  Yu Liu,et al.  Dynamic fault tree analysis based on continuous-time Bayesian networks under fuzzy numbers , 2015 .

[23]  Weiwen Peng,et al.  Reliability assessment of complex electromechanical systems under epistemic uncertainty , 2016, Reliab. Eng. Syst. Saf..

[24]  Marko Cepin,et al.  A new method for explicit modelling of single failure event within different common cause failure groups , 2012, Reliab. Eng. Syst. Saf..

[25]  M. Benguediab,et al.  Reliability evaluation of electrical power systems including multi-state considerations , 2006 .

[26]  Yongshou Liu,et al.  Hybrid reliability analysis with both random and probability-box variables , 2015 .

[27]  David W. Coit,et al.  Composite importance measures for multi-state systems with multi-state components , 2005, IEEE Transactions on Reliability.

[28]  Ramana V. Grandhi,et al.  Comparison of evidence theory and Bayesian theory for uncertainty modeling , 2004, Reliab. Eng. Syst. Saf..

[29]  Hong-Zhong Huang,et al.  Reliability analysis of multi-state systems with common cause failure based on Bayesian Networks , 2012, 2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering.

[30]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[31]  Jian Guo,et al.  Multisensor Data Fusion for Water Quality Evaluation Using Dempster-Shafer Evidence Theory , 2013, Int. J. Distributed Sens. Networks.

[32]  Hong-Zhong Huang,et al.  Fuzzy Sets Method of Reliability Prediction and Its Application to a Turbocharger of Diesel Engines , 2013 .

[33]  Philippe Weber,et al.  Evidential Networks for Reliability Analysis and Performance Evaluation of Systems With Imprecise Knowledge , 2009, IEEE Transactions on Reliability.