Component importance measures for complex repairable system

In recent years, the system signature has been recognized as an important tool to quantify the reliability of systems consist of independent and identically distributed (iid) or exchangeable components with respect the random failure times. System signature separates the system structure from the component probabilistic failure distribution. However, when it is adopted to solve a complex system with more than one component type, it requires the computation of the probabilities of all possible different ordering statistics of each component failure lifetime distributions, which is often an intractable procedure.