How can we use Birnbaum importance measure for complicated systems in reliability?

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Birnbaum importance measure is used when we are provided the survival probabilities of all the components in a coherent system. It is the rate of increase in the system reliability with respect to the increase in component reliability. I studied some application of this method in series and parallel systems , but couldn't find any use of this method in complicated problems...
Do we need any decomposition methods like tie-set or cut-set for these problems? for example if we have this system: a complicated system