Calculation of importance measure of multi-state phased-mission systems with cascading effect

Importance measure refers to the degree to which the system performance is affected by the failure or state change of single or few components in the system. It can be used to reasonably allocate detection and maintenance resources, so as to guarantee the common operation of the most important components in system. Traditional importance measures could not evaluate the multi-state phased-mission system (MS-PMS) with cascading effect. Then we propose a method to calculate the multi-state Birnbaum importance, reliability achievement worth, risk reduction worth and Fussell-Vesely importance of MS-PMS with cascading effect. Finally, we give a numerical example to verify this combination way.