<abstract><p>We consider a mixed system with $ n $ components, where at time $ t, $ all system components are functioning. We then use the system signature to evaluate the extropy of the excess lifetime of the mixed system, which is a useful criterion for predicting the lifetime of the system. We give several results including expressions, bounds, and order conditions for the above measure. Finally, based on the relative extropy, we establish a criterion for selecting a preferred system that is closely related to the parallel system.</p></abstract>