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

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, c, c). (2) Three-class plans (m, M, c, c) tend to have nearly the same slope for the OC-function as two-class plans (m, c). 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. (3) Three-class plans imply the principle of zero tolerance. As a consequence, in a heterogeneous lot one extreme result determines the acceptance or rejection of the whole lot, and the consumer's risk tends to be reduced.