We investigated the possibility that Logistic Regression Functions (LRFs), when used in combination with Boolean Discriminant Functions (BDFs), which we had previously developed, would improve the quality classification ability of BDFs when used alone. This was the case; when the union of a BDF and LRF was used to classify quality, the predicative accuracy of quality and inspection cost was improved over that of using either function alone for the Space Shuttle. Also, the LRFs proved useful for ranking the quality of modules in a build. The significance of these results is that very high quality classification accuracy (1.25% error) can be obtained while reducing the inspection cost incurred in achieving high quality. This is particularly important for safety critical systems. Because the methods are general and not particular to the Shuttle, they could be applied to other domains. A key part of the LRF development was a method for identifying the critical value (i.e. threshold) that could discriminate between high and low quality and at the same time constrain the cost of inspection to a reasonable value.