The distribution of a coherent system based on IID components can be written as a mixture of the distributions of progressively Type‐II censored order statistics. The coefficients in that representation are called the progressive censoring signature (PC‐signature) of the system. In this paper, we explore the basic properties and potential applications of these mixture representations. We show that they can be used to study the associated censoring schemes (and their exact probabilities) in the operating development of the system. It is illustrated that, in some sense, the PC‐signature provides more information than the classical (Samaniego) signature of the system. Further, this new signature can be used to establish distribution‐free ordering properties for system lifetimes. Copyright © 2016 John Wiley & Sons, Ltd.