Some statistical aspects of binary measuring systems

Qualitative analysis is often used to determine whether or not a particular feature appears or is absent in tests, in quality control procedures, identification scans, go/no go measurements and many other fields. Generally, such analysis uses simple measuring methods that classify the analyzed property value into two comprehensive and exclusive classes/categories. The performance reliability of such binary measurement systems (BMSs) is usually assessed by false positive and false negative rates. The article presents some additional aspects related to metrological properties of BMS: traceability – described in terms of sequential hierarchical chain of consecutive BMSs calibrations – error accumulation, distribution of test results, consistency and repeatability problems. It is shown that some intuitively plausible at a first glance concepts such as hypotheses about the binomial distribution of test results or consistency testing by sequentially repeated sorting are wrong if the objective is to conduct a deep examination, and therefore, should be avoided.

► We analyzed statistical metrological properties of binary measuring systems (BMSs).
► The proposed traceability model allows the BMS’ error rates to be simply assessed.
► The distribution of the objects classified by BMS is found to be far from binomial.
► Calibration based on a contingency table method is proposed as the most evidentiary.
► The practice of checking accuracy by sequent repeated sorting is shown to be faulty.