Importances of components and events in non-coherent systems and risk models

• Extensions of importance measures to noncoherent systems.
• Focus on Birnbaum and Criticality importances and Risk Gains.
• Importances with respect to system unavailabilities and failure intensities.
• Relationships, comparisons and interpretations of importance measures.
• Effective quantification, numerical examples and comparisons to earlier methods.

Component importance measures have been defined and applied so far mostly for coherent systems. This paper develops and compares possible extensions of the traditional measures to non-coherent systems. The focus is on Birnbaum- and Criticality-type importances, both with respect to system unavailability and system failure intensity. Several versions are suggested for both measure types, each with different interpretation and potential applications. The measures are presented in terms of Boolean system logic functions so that they can be quantified with usual fault tree techniques even for large systems without manually solving and derivation of lengthy analytical functions. Examples demonstrate the method and discover some potential problems in system design if a component can initiate an accident while it is also part of a safety function to prevent an accident. Results are compared to earlier published results obtained with different algorithms.