Considering a semicoherent system made up of n components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the n-tuple whose kth coordinate is the probability that the kth component failure causes the system to fail. This n-tuple, which depends only on the...

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow–Proschan importance index. Specifically, given a nonempty subset M of the set of components of a system, we define the M-signature of the system as the...

The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow–Proschan importance index. These indexes can be computed through explicit linear expressions involving the values of the structure...

We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear combinations of order statistics, and lattice polynomials, are...