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.