The study examines the rule space model, a probabilistic model capable of measuring cognitive skill acquisition and of diagnosing erroneous rules of operation in a procedural domain. The model involves two important components: (1) determination of a set of bug distributions (bug density functions representing clusters around the rules); and (2) establishment of decision rules for classifying an observed response pattern into one of the clusters around the rules and computing error probabilities. This study further discusses the theoretical foundation of the model by introducing "bug distribution" and hypothesis testing (Bayes' decision rules for minimum errors). The model does not require a large-scale computation. It is helpful in areas of research and teaching. It can be used with microcomputers for testing hypotheses and validating data with probabilistically-sound information, and it can improve and modify information for the cluster ellipses as more students are added to research projects. (LMO)