  It is known that the Barlow-Proschan index of a system with i.i.d. component
lifetimes coincides with the Shapley value, a concept introduced earlier in
cooperative game theory. Due to a result by Owen, this index can be computed
efficiently by integrating the first derivatives of the reliability function of
the system along the main diagonal of the unit hypercube. The Samaniego
signature of such a system is another important index that can be computed for
instance by Boland's formula, which requires the knowledge of every value of
the associated structure function. We show how the signature can be computed
more efficiently from the diagonal section of the reliability function via
derivatives. We then apply our method to the computation of signatures for
systems partitioned into disjoint modules with known signatures.
