Integrated importance measure for multi-state coherent systems of k level

To verify the effectiveness of the integrated importance measure (IIM) for multi-state coherent systems of k level, the definition and physical meaning of IIM are demonstrated. Then, the improvement potential and ¿-importance measures are generalized to multi-state coherent systems based on the system performance level, and the relationships between IIM and traditional importance measures are discussed. The characteristics of IIM are demonstrated in both series and parallel systems. Also, an application to an oil transportation system is given. The comparison results show that: (i) IIM has some useful properties that are not possessed by traditional importance measures; (ii) IIM is effective in evaluating the component role in multi-state systems when the component reliability and the failure rate are simultaneously considered.