A one-sided single screening procedure based on individual unit misclassification error

Abstract

A procedure is proposed for screening applications in quality control that eliminates overselection (namely, the condition where the proportion of accepted screened items is greater than the proportion of conforming items in the original population) and controls for individual unit misclassification error (IME), namely, the probability of an accepted/selected item being below specification. Screening involves selecting items whose performance is within specifications based on observing one or more correlated screening variables in lieu of observing the performance variable directly. Overselection and an uncontrollably high IME can occur when (1) there is a high correlation between the performance and screening variables and (2) the proportion of conforming items among accepted items (or its complement, average outgoing quality (AOQ)), is prespecified as in, for example, Owen et al. (1975). We instead propose a procedure that prespecifies a maximum tolerable IME (emaxa) for accepted items, which eliminates overselection and assures that the IME of each outgoing item as well as the AOQ are both equal to or less than emaxa. The quality of each individual item as well as AOQ is thereby explicitly controlled. Only the use of standard normal tables is required to implement our proposed procedure.

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