SINGLE AND DOUBLE SCREENING PROCEDURES USING INDIVIDUAL MISCLASSIFICATION ERROR IN QUALITY CONTROL (BIVARIATE, APPROXIMATION)

HSIEN-TANG TSAI, Purdue University

Abstract

The individual misclassification error (IME) is introduced to the problem of screening in quality control which is to select the items whose performance is within specifications by observing one or more correlated screening variables instead of the performance variable directly. A new single screening, in which the maximum IME (emaxa) for those accepted items is prespecified, is proposed to overcome the following two problems associated with the screening procedure proposed by Owen, McIntire and Seymour (OMS) (1975): (1) the emaxa increases as the correlation between screening and performance variables increases, and (2) over selection occurs when the correlation is large. One can thus claim that each outgoing item's IME and average outgoing quality (AOQ) are both less than or equal to the emaxa. Screening using multiple screening variables is considered as well. Another advantage of prespecifying an emaxa is that a double screening procedure (DSP) can be constructed. Suppose there are two screening variables available to predict the performance variable. One screening variable is used first to make one of three decisions--acceptance, undecided, or rejection--according to the magnitude of the IME. After the first screening, the second screening variable is employed to filter the undecided items. A manufacturer thus not only can control the IME and AOQ, but also save considerable time, effort and inspection cost. The bivariate normal distribution is frequently employed as a model for the problem of screening, but the computational formulae for bivariate normal probabilities are quite complicated. An approximation for cumulative standard bivariate normal probabilities is developed using a polynomial approximation of the standard univariate normal distribution. Our approximation is particularly appropriate for the application of a screening procedure in quality control, because it is most accurate with large absolute correlation coefficients. Since a univariate normal polynomial approximation is needed for approximating bivariate normal probabilities, a systematic approach for constructing a 3-interval polynomial approximation for a continuous univariate distribution function is proposed. The software code for this approximation is also provided.

Degree

Ph.D.

Subject Area

Management

COinS