A formulation of the concept of quality factor based on the microdosimetric quantity lineal energy, y, is described. Toward this end, functions--denoted Specific Quality Functions (SQF)--are defined such that (a) they can be determined directly from observation and (b) a number of them can be used toward setting, by consensus, the values of a microdosimetrically-based quality factor. The determination of SQFs is exemplified by correlating data on the yields of dicentric aberrations in human lymphocytes with measured and calculated microdosimetric distributions. The implications of this approach to problems of radiation protection are discussed.