This Bureau of Mines report proposes a new methodology for estimating industrial dust explosion hazards in terms of three probabilities or cofactors: the dispersion of the dust, the existence of a flammable dust concentration, and the presence of an effective source of ignition. This method or rationale is proposed as a replacement for the "explosibility index" that was first suggested 25 yr ago, but which, by consensus among leading researchers in the field, is now outdated. This report presents a detailed critique of the deficiencies of that old, material-oriented index, and develops the logical rationale for its replacement by an approach that is better suited for quantitative hazard evaluations. A variety of such evaluations are illustrated that show how a quantitative prediction of explosion frequencies can be obtained from laboratory measurements and operating conditions in a given industrial facility. The method has some pitfalls, particularly as they relate to the correlations of events or their randomness. These are discussed, as well as the method's other limitations and uncertainties. This work is intended to provide a beginning to a quantitative approach to explosion hazard assessment. To that end, a new method is proposed for estimating thermal ignition in terms of the measured laboratory autoignition temperature of a dust, its relationship to the operating temperature, and its distribution within a given industrial system.