Relationship and Changing Analysis of Birnbaum Importance for Different Components with Bayesian Networks

Abstract Importance measures are widely used in reliability engineering. To support system reliability optimization, this paper studies the relationship and changing characteristics of the Birnbaum importance measures (BMs) for different components in binary coherent systems. First, the probabilistic meaning of BM and a modeling method for binary coherent system based on Bayesian network (BN) are presented. Then, the relationship of BMs for different components is explored according to the position of corresponding nodes (components) in BN structures. Later, the changing of BMs for different components, which is caused by the reliability improvements of related root or middle nodes (components) in BN structures, is analyzed respectively. Finally, an illustrative example of a helicopter convertor is implemented to demonstrate the calculation and application process of the relationship and changing characteristics in binary coherent systems with BN. The experimental analysis results substantiate the correctness and effectiveness of the proposed relationship and changing characteristics of BMs for different components.

[1]  Wei Li,et al.  A Framework for Reliability Approximation of Multi-State Weighted $k$-out-of-$n$ Systems , 2010, IEEE Transactions on Reliability.

[2]  Lirong Cui,et al.  NEW COMPARISONS IN BIRNBAUM IMPORTANCE FOR THE CONSECUTIVE- k -OUT-OF- n SYSTEM , 1999 .

[3]  Luca Podofillini,et al.  Generalised importance measures for multi-state elements based on performance level restrictions , 2003, Reliab. Eng. Syst. Saf..

[4]  Irad Ben-Gal,et al.  Efficient Bayesian Network Learning for System Optimization in Reliability Engineering , 2012 .

[5]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[6]  W. E. Vesley.  A Time Dependent Methodology for Fault Tree Evaluation , 1970 .

[7]  Emanuele Borgonovo,et al.  The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions , 2010, Eur. J. Oper. Res..

[8]  F. C. Meng,et al.  Component-relevancy and characterization results in multistate systems , 1993 .

[9]  Lirong Cui,et al.  Analysis for joint importance of components in a coherent system , 2007, Eur. J. Oper. Res..

[10]  Philippe Weber,et al.  Complex system reliability modelling with Dynamic Object Oriented Bayesian Networks (DOOBN) , 2006, Reliab. Eng. Syst. Saf..

[11]  Christophe Bérenguer,et al.  Reliability importance analysis of Markovian systems at steady state using perturbation analysis , 2008, Reliab. Eng. Syst. Saf..

[12]  W. E. Vesely,et al.  A time-dependent methodology for fault tree evaluation , 1970 .

[13]  Nader Ebrahimi,et al.  Multistate reliability models , 1984 .

[14]  Benoît Iung,et al.  Formalisation of a new prognosis model for supporting proactive maintenance implementation on industrial system , 2008, Reliab. Eng. Syst. Saf..

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

[16]  Lakhmi C. Jain,et al.  Introduction to Bayesian Networks , 2008 .

[17]  Shenggui Zhang,et al.  Integrated importance measures of multi-state systems under uncertainty , 2010, Comput. Ind. Eng..

[18]  M. Cheok,et al.  Use of importance measures in risk-informed regulatory applications , 1998 .

[19]  Z W Birnbaum,et al.  ON THE IMPORTANCE OF DIFFERENT COMPONENTS IN A MULTICOMPONENT SYSTEM , 1968 .

[20]  Emanuele Borgonovo.  Differential, criticality and Birnbaum importance measures: An application to basic event, groups and SSCs in event trees and binary decision diagrams , 2007, Reliab. Eng. Syst. Saf..

[21]  Howard E. Lambert.  Fault Trees for Decision Making in Systems Analysis , 2013 .

[22]  J. B. Fussell,et al.  How to Hand-Calculate System Reliability and Safety Characteristics , 1975, IEEE Transactions on Reliability.

[23]  Shaomin Wu,et al.  Performance utility-analysis of multi-state systems , 2003, IEEE Trans. Reliab..

[24]  F. Proschan,et al.  Importance of System Components and Fault Tree Events. , 1975 .

[25]  C. Lie,et al.  Joint reliability-importance of two edges in an undirected network , 1993 .

[26]  Luca Podofillini,et al.  Importance Measures of Multi-State Components in Multi-State Systems , 2003 .

[27]  Shaomin Wu,et al.  Joint importance of multistate systems , 2005, Comput. Ind. Eng..