<p>Recent research has shown growing interest in quantifying uncertainty in system lifetimes. This paper investigates the failure extropy (FEx) of an <i>n</i>-component mixed system, conditioned on the failure of all components by a given time <i>t.</i> Using the concept of system signature, explicit expressions for the FEx of the system lifetime are derived, along with key properties and informative bounds. To extend this framework, a divergence measure based on FEx is proposed to assess the complexity of system structures. A new discrimination measure is also proposed, serving as a valuable tool to assess how closely a system resembles a parallel system. An application to redundancy allocation has been carried out to demonstrate the practical relevance of the proposed results and provide insights into optimal system design under uncertainty.</p>