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The search for a bona fide robustness index to quantify the system performance upon unexpected disturbances has been a continuous research effort. Previous studies have largely neglected to reflect the damage evolution feature of a progressive collapse failure. To bridge this important knowledge gap, this paper presents a novel risk-based robustness index for structures prone to disproportionate progressive collapse. Defined on a new concept, referred to as damage evolution curve, the proposed index considers the full spectrum of risk due to initiating events, and rigorously quantifies the impact of intermediate partial damages on the robustness assessment. Examples using a Daniels system, a truss, and an idealised moment-resistant frame are presented to illustrate how the proposed index is applied for assessing the robustness of structures with increasing complexity. In addition, a comprehensive comparative study against four existing robustness indices is carried out. It is shown that the proposed index provides consistent results for different influencing factors, whereas the other indices either respond counter-intuitively or are insensitive to some of the factors. With consideration of intermediate damage and failure consequences, the development of the proposed robustness index represents an important step towards the performance-based design against progressive collapse. [ABSTRACT FROM AUTHOR]