The Samaniego signature is a relevant tool for studying the performance of a system whose component lifetimes are exchangeable. It is well known that the stochastic ordering of the signatures of two systems implies the same for the respective system lifetimes. We prove that the reverse claim is not true when the component lifetimes are independent and identically distributed. There exist small proportions of systems with stochastically ordered lifetimes whose signatures are not ordered. We present a simple procedure in order to check whether the system lifetimes are stochastically ordered even if their signatures are not comparable.

We consider semicoherent and mixed systems with exchangeable components. We present sharp lower and upper bounds on various dispersion measures (in particular, variance and median absolute deviation) of the system lifetime, expressed in terms of the system signature and the dispersion of a single component lifetime. We construct joint exchangeable distributions of component lifetimes with two-point marginals which attain the bounds in the limit.

We consider coherent and mixed reliability systems composed of elements with independent and identically distributed lifetimes. We present upper bounds on variances of system lifetimes, expressed in terms of variances of single components. We also discuss attainability conditions and some special cases and examples.