Quantitative analysis of dynamic fault trees using improved Sequential Binary Decision Diagrams

Dynamic fault trees (DFTs) are powerful in modeling systems with sequence- and function dependent failure behaviors. The key point lies in how to quantify complex DFTs analytically and efficiently. Unfortunately, the existing methods for analyzing DFTs all have their own disadvantages. They either suffer from the problem of combinatorial explosion or need a long computation time to obtain an accurate solution. Sequential Binary Decision Diagrams (SBDDs) are regarded as novel and efficient approaches to deal with DFTs, but their two apparent shortcomings remain to be handled: That is, SBDDs probably generate invalid nodes when given an unpleasant variable index and the scale of the resultant cut sequences greatly relies on the chosen variable index. An improved SBDD method is proposed in this paper to deal with the two mentioned problems. It uses an improved ite (If-Then-Else) algorithm to avoid generating invalid nodes when building SBDDs, and a heuristic variable index to keep the scale of resultant cut sequences as small as possible. To confirm the applicability and merits of the proposed method, several benchmark examples are demonstrated, and the results indicate this approach is efficient as well as reasonable.

[1]  Salvatore J. Bavuso,et al.  Dynamic fault-tree models for fault-tolerant computer systems , 1992 .

[2]  David He,et al.  Analysis of sequential failures for assessment of reliability and safety of manufacturing systems , 2002, Reliab. Eng. Syst. Saf..

[3]  Liudong Xing,et al.  Reliability Analysis of Nonrepairable Cold-Standby Systems Using Sequential Binary Decision Diagrams , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[4]  Hao Chen,et al.  A Stochastic Computational Approach for Accurate and Efficient Reliability Evaluation , 2014, IEEE Transactions on Computers.

[5]  Suprasad V. Amari,et al.  A new approach to solve dynamic fault trees , 2003, Annual Reliability and Maintainability Symposium, 2003..

[6]  Jean-Jacques Lesage,et al.  Algebraic determination of the structure function of Dynamic Fault Trees , 2011, Reliab. Eng. Syst. Saf..

[7]  Mariëlle Stoelinga,et al.  A Rigorous, Compositional, and Extensible Framework for Dynamic Fault Tree Analysis , 2010, IEEE Transactions on Dependable and Secure Computing.

[8]  Mansoor Alam,et al.  Quantitative Reliability Evaluation of Repairable Phased-Mission Systems Using Markov Approach , 1986, IEEE Transactions on Reliability.

[9]  John N. Tsitsiklis,et al.  Introduction to Probability , 2002 .

[10]  Meng Lin,et al.  SFRs-based numerical simulation for the reliability of highly-coupled DFTS , 2015 .

[11]  Antoine Rauzy,et al.  BDD Based Fault-Tree Processing , 1997 .

[12]  C. Y. Lee Representation of switching circuits by binary-decision programs , 1959 .

[13]  Ferdinando Chiacchio,et al.  A Weibull-based compositional approach for hierarchical dynamic fault trees , 2013, Reliab. Eng. Syst. Saf..

[14]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[15]  Dong Li,et al.  Quantification of Highly Coupled Dynamic Fault Tree Using IRVPM and SBDD , 2016, Qual. Reliab. Eng. Int..

[16]  Dong Liu,et al.  Quantification of Cut Sequence Set for Fault Tree Analysis , 2007, HPCC.

[17]  Ferdinando Chiacchio,et al.  Dynamic fault trees resolution: A conscious trade-off between analytical and simulative approaches , 2011, Reliab. Eng. Syst. Saf..

[18]  Antoine Rauzy,et al.  New algorithms for fault trees analysis , 1993 .

[19]  Ming Jian Zuo,et al.  A Stochastic Approach for the Analysis of Fault Trees With Priority AND Gates , 2014, IEEE Transactions on Reliability.

[20]  Peng Zhang,et al.  Reliability Evaluation of Phasor Measurement Unit Using Monte Carlo Dynamic Fault Tree Method , 2012, IEEE Transactions on Smart Grid.

[21]  J.B. Fussell,et al.  On the Quantitative Analysis of Priority-AND Failure Logic , 1976, IEEE Transactions on Reliability.

[22]  Jean-Jacques Lesage,et al.  Quantitative Analysis of Dynamic Fault Trees Based on the Structure Function , 2014, Qual. Reliab. Eng. Int..

[23]  Daochuan Ge,et al.  Probabilistic model–based multi-integration formulas for quantifying a generalized minimal cut sequence , 2015 .

[24]  Liudong Xing,et al.  Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures , 2011, Reliab. Eng. Syst. Saf..

[25]  Yves Dutuit,et al.  A linear-time algorithm to find modules of fault trees , 1996, IEEE Trans. Reliab..

[26]  J. Dugan,et al.  A modular approach for analyzing static and dynamic fault trees , 1997, Annual Reliability and Maintainability Symposium.

[27]  Seyed Ghassem Miremadi,et al.  FPGA-based Monte Carlo simulation for fault tree analysis , 2004, Microelectron. Reliab..

[28]  Salvatore J. Bavuso,et al.  Fault trees and Markov models for reliability analysis of fault-tolerant digital systems , 1993 .

[29]  Shigeru Yanagi,et al.  Quantitative analysis of a fault tree with priority AND gates , 2008, Reliab. Eng. Syst. Saf..

[30]  Claude E. Shannon,et al.  A symbolic analysis of relay and switching circuits , 1938, Transactions of the American Institute of Electrical Engineers.

[31]  Jean-Jacques Lesage,et al.  Probabilistic Algebraic Analysis of Fault Trees With Priority Dynamic Gates and Repeated Events , 2010, IEEE Transactions on Reliability.

[32]  Liang Yin,et al.  Hierarchical composition and aggregation of state-based availability and performability models , 2003, IEEE Trans. Reliab..