Three-Class Attributes Plans in Microbiological Quality Control: A Contribution to the Discussion

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Abstract
In this study, the structure of two- and three-class attributes plans is explained and their decision-making process is illustrated by practical examples. Further, the selectivity of attributes plans is compared to that of variables plans by analyzing the corresponding operating-characteristic (OC) curves. Based on the statistical analysis presented, the following conclusions are drawn: (1) Three-class plans are lacking in clarity, because the decision-making process is influenced in a complex way by the relations between variance within a lot, the distance between m and M, and the choice of the maximum allowable number of defectives (acceptance number, cm, cM). (2) Three-class plans (m, M, cm, cM) tend to have nearly the same slope for the OC-function as two-class plans (m, cm). They show less stringency than analogous variables plans (mean-value plans) with known variance and seem to show no marked difference in stringency compared to analogous variables plans in case the variance has to be estimated. (...

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