This communication proposes a new relationship for estimation of the damage factor (DF) used in the Dow Fire and Explosion Index (F&EI). The proposed new relation more clearly shows how the damage factor depends on other factors in the F&EI, such as material factor (MF) and Process Unit Hazards Factor, and leads to the definition of a new index which accounts for loss control measures implemented in the plant, and thus gives a measure of risk. Analysis shows that three types of relations exist between DF and Process Unit Hazards Factor depending on the size of the MF-low, medium or high. Further analysis shows, that the procedure in the current F&EI Guide may overestimate the DF for a very low MF and moderate to high Process Unit Hazards Factor. The analysis leads to the definition of the Likely Loss Fire & Explosion Index, which provides an estimate of risk of losses from fires and explosions as well as degrees of risk similar to the estimate of hazards and degrees of hazard associated with the Fire & Explosion Index.