Statistical Methods for Thematic-Accuracy Quality Control Based on an Accurate Reference Sample

The goal of this work is to present a set of statistical tests that offer a formal procedure to make a decision as to whether a set of thematic quality specifications of a product is fulfilled within the philosophy of a quality control process. The tests can be applied to classification data in thematic quality control, in order to check if they are compliant with a set of specifications for correctly classified elements (e.g., at least 90% classification correctness for category A) and maximum levels of poor quality for confused elements (e.g., at most 5% of confusion is allowed between categories A and B). To achieve this objective, an accurate reference is needed. This premise entails changes in the distributional hypothesis over the classification data from a statistical point of view. Four statistical tests based on the binomial, chi-square, and multinomial distributions are stated, to provide a range of tests for controlling the quality of product per class, both categorically and globally. The proposal is illustrated with a complete example. Finally, a guide is provided to clarify the use of each test, as well as their pros and cons.