Joint Failure-Importance of Components in Fault Tree

Hong & Lie (1993) defined joint failure importance(JFI) as a measure of how 2 components in a system interact in contributing to the system failure. Their definitions were given on the basis of Birnbaum importance, but there are some contradictions of the calculation for fault tree analysis. Hong's importance measures mainly concern the 2 components' position in the system and interrelationship. However, they are difficult to describe how much the probability of system failure is influenced by component failures. Therefore, JFI could not give the correct numerical order of weak components. Thus, this paper: 1) gives an explicit formula for the improved JFI. This utility importance overcomes some drawbacks of a well-known importance measure suggested by J.S. Hong, 2) proves the improved JFI is always non-negative for some classes of systems, 3) illustrates computed results with numerical examples.