Signature Conditions for Distributional Properties of System Lifetimes if Component Lifetimes are I.I.D. Exponential

In this article, we consider coherent and mixed systems built of components with independent identically exponentially distributed lifetimes. We establish various sufficient and necessary conditions on the system signatures for asserting strong unimodality of the system lifetime as well as the monotonicity of its failure rate and mean residual life. Our investigations show that the precise description of the conditions characterizing the above distributional properties of the system lifetimes in the classic exponential model is a challenging task.