IN SAMPLING inspection by attributes, each item is classified simply as defective or non-defective, with several different quality characteristics ordinarily considered in making this classification. Very often, the types of possible defects are collected into groups and sampling plans are applied to each group separately. But even within a group there may be numerous equally important sources of defects. For example, in the manufacture of aircraft bolts, defects are classified as critical, major, minor A, and minor B. In the major group there are as many as 13 possible sources of defects, i.e., thread size and form, grip length, plating, etc. Characteristics also may be assigned to groups according to their position in the production process, e.g., in the manufacture of radio receivers natural inspection stations may arise during different stages of the process. In any case, for a given group of more or less equally important types of defects it may be desirable for the vendor or the consumer to inspect a lot for different types of defects during different stages of the production process. In the first place, lots that are certain to be eventually rejected should be caught early and subsequent fabrication costs saved. Lots of radio receivers that are bad should be rejected in the production process as early as possible. Secondly, manufacturers are interested in the cause of trouble whenever any arises. If lots of aircraft bolts are rejected, with one of the thirteen characteristics mainly responsible (e.g., more than two imperfect threads), the manufacturer wants to have this information. Finally, further operations in a process may hide defects. In the assembly of radio receivers, additional operations could easily obscure a poorly soldered joint. Painting or plating could prevent identification of surface flaws. It often is necessary that, if characteristics are considered separately, the resulting protection measured in terms of the Operating Characteristic (OC) curve (i.e., for a given sampling procedure and incoming quality, the probability of accepting the lot) should be the same as that which would be achieved if all the characteristics were considered together since, (1) the purchaser may be interested in over-all quality within each group, (2) suppliers, though interested in individual char-