Dynamic Fault Tree Analysis Using Bayesian Networks and Sequence Probabilities

Tetsushi YUGE; Shigeru YANAGI

doi:10.1587/transfun.E96.A.953

Dynamic Fault Tree Analysis Using Bayesian Networks and Sequence Probabilities

Tetsushi YUGE, Shigeru YANAGI

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A method of calculating the exact top event probability of a fault tree with dynamic gates and repeated basic events is proposed. The top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, the Markov-based method is not realistic for a complex system model because the number of states that should be considered in the Markov analysis increases explosively as the number of basic events in the model increases. To overcome this shortcoming, we propose an alternative method in this paper. It is a hybrid of a Bayesian network (BN) and an algebraic technique. First, modularization is applied to a dynamic fault tree. The detected modules are classified into two types: one satisfies the parental Markov condition and the other does not. The module without the parental Markov condition is replaced with an equivalent single event. The occurrence probability of this event is obtained as the sum of disjoint sequence probabilities. After the contraction of modules without parent Markov condition, the BN algorithm is applied to the dynamic fault tree. The conditional probability tables for dynamic gates are presented. The BN is a standard one and has hierarchical and modular features. Numerical example shows that our method works well for complex systems.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.5 pp.953-962

Publication Date: 2013/05/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E96.A.953

Type of Manuscript: PAPER

Category: Reliability, Maintainability and Safety Analysis

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Tetsushi YUGE, Shigeru YANAGI, "Dynamic Fault Tree Analysis Using Bayesian Networks and Sequence Probabilities" in IEICE TRANSACTIONS on Fundamentals, vol. E96-A, no. 5, pp. 953-962, May 2013, doi: 10.1587/transfun.E96.A.953.
Abstract: A method of calculating the exact top event probability of a fault tree with dynamic gates and repeated basic events is proposed. The top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, the Markov-based method is not realistic for a complex system model because the number of states that should be considered in the Markov analysis increases explosively as the number of basic events in the model increases. To overcome this shortcoming, we propose an alternative method in this paper. It is a hybrid of a Bayesian network (BN) and an algebraic technique. First, modularization is applied to a dynamic fault tree. The detected modules are classified into two types: one satisfies the parental Markov condition and the other does not. The module without the parental Markov condition is replaced with an equivalent single event. The occurrence probability of this event is obtained as the sum of disjoint sequence probabilities. After the contraction of modules without parent Markov condition, the BN algorithm is applied to the dynamic fault tree. The conditional probability tables for dynamic gates are presented. The BN is a standard one and has hierarchical and modular features. Numerical example shows that our method works well for complex systems.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.953/_p

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@ARTICLE{e96-a_5_953,
author={Tetsushi YUGE, Shigeru YANAGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Dynamic Fault Tree Analysis Using Bayesian Networks and Sequence Probabilities},
year={2013},
volume={E96-A},
number={5},
pages={953-962},
abstract={A method of calculating the exact top event probability of a fault tree with dynamic gates and repeated basic events is proposed. The top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, the Markov-based method is not realistic for a complex system model because the number of states that should be considered in the Markov analysis increases explosively as the number of basic events in the model increases. To overcome this shortcoming, we propose an alternative method in this paper. It is a hybrid of a Bayesian network (BN) and an algebraic technique. First, modularization is applied to a dynamic fault tree. The detected modules are classified into two types: one satisfies the parental Markov condition and the other does not. The module without the parental Markov condition is replaced with an equivalent single event. The occurrence probability of this event is obtained as the sum of disjoint sequence probabilities. After the contraction of modules without parent Markov condition, the BN algorithm is applied to the dynamic fault tree. The conditional probability tables for dynamic gates are presented. The BN is a standard one and has hierarchical and modular features. Numerical example shows that our method works well for complex systems.},
keywords={},
doi={10.1587/transfun.E96.A.953},
ISSN={1745-1337},
month={May},}

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TY - JOUR
TI - Dynamic Fault Tree Analysis Using Bayesian Networks and Sequence Probabilities
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 953
EP - 962
AU - Tetsushi YUGE
AU - Shigeru YANAGI
PY - 2013
DO - 10.1587/transfun.E96.A.953
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2013
AB - A method of calculating the exact top event probability of a fault tree with dynamic gates and repeated basic events is proposed. The top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, the Markov-based method is not realistic for a complex system model because the number of states that should be considered in the Markov analysis increases explosively as the number of basic events in the model increases. To overcome this shortcoming, we propose an alternative method in this paper. It is a hybrid of a Bayesian network (BN) and an algebraic technique. First, modularization is applied to a dynamic fault tree. The detected modules are classified into two types: one satisfies the parental Markov condition and the other does not. The module without the parental Markov condition is replaced with an equivalent single event. The occurrence probability of this event is obtained as the sum of disjoint sequence probabilities. After the contraction of modules without parent Markov condition, the BN algorithm is applied to the dynamic fault tree. The conditional probability tables for dynamic gates are presented. The BN is a standard one and has hierarchical and modular features. Numerical example shows that our method works well for complex systems.
ER -