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There exist several risk importance measures in the literature to rank the relative importance among basic events within a fault tree. Most of the importance measures indicate how important a basic event is with respect to the top event of the fault tree. However, the mutual influence among the basic events should also be considered. This is particularly true in practice when making maintenance decisions with a limited resource. This paper investigates the Joint Failure Importance (JFI), which reflects the interaction among basic events, namely, the change in the Birnbaum Importance of one basic event when the probability of another basic event changes. Even though the JFI for coherent fault trees and its properties have been examined in the literature, the results cannot be easily extended to noncoherent fault trees. The current work has shown that, for both coherent, and noncoherent fault trees, the sign of the JFI can provide useful information. However, the properties of the JFI for noncoherent fault trees are more complex, and do not always share with those for coherent fault trees. The Shutdown System Number One (SDS1) in a Canadian Deuterium-Uranium (CANDU) Nuclear Power Plant (NPP) is utilized to illustrate the theoretical results developed in this paper.