In the general problem of quantitative NDE, the majority of past approaches are based upon the questionable assumption that the dominant defect or flaw can be identified before the beginning of the main body of the analysis. This concept is fundamental to most (but not all) treatments of probabilistic failure prediction and accept/reject optimization. This oversimplification and associated logical tangles are obviated by a more comprehensive approach to defect characterization and probabilistic failure prediction, in which it is assumed in the pertinent stochastic models that the various significant types of defects occur in all possible numbers. In this paper, we present a version of such an approach that involves a single type of defect and a promising approximation methodology.