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...following reasons: process of measuring Y is destructive or will degrade the product (e.g., the life testing of bulbs or durability testing of vehicle tires); (ii) it is too expensive to measure Y (e.g., the measurement of the pressure inside a rocket); (iii) the value of the performance variable is revealed only in subsequent product use (e.g., the estimation of gasoline yields from crude oil); and (iv) it is a method by which considerable inspection cost will be saved (e.g., if there exist two performance variables which are correlated, one is used as a screening variable for the other. Then only one of the performance variables needs to be tested). The screening problem is to select items within a given specification by observing screeni ng variables that are correlated with the performance variable Y. In order to save on inspection costs, a sequential screening procedure based on the Individual Misclassification Error (IME) technique of Tsai (1986) is developed. The problem of overselection can be avoided by controlling the appropriate IME. An example with four screening variables allocated into single-stage, double-stage and triple-stage sequential screening procedures (SSP, DSP and TSP) is given for illustration.
2. Literature review
Taylor and Russel (1939) were the pioneers of the area of screening procedures in manufacturing industries. Lipow and Eidemiller (1964) developed a screening model under the consideration of saving costs. Owen et al. (1975) compiled usable tables and a methodology for when there are one or two screening variables under the assumption of normal distribution for one-sided specification. Owen and Boddie (1976) solved the screening problem when the parameters are unknown. Owen and Su (1977) solved the screening problem when the correlation coefficient of the performance variable and the screening variable are unknown. Subsequently, Thomas et al. (1977), Li and Owen (1979), Oden and Owen (1980), Owen, Li and Chou (1981) and Madsen (1982) have extended the original work of Owen et al. (1975). Wang et al. (1985) investigated the screening problem using a Bayesian approach. Tang and Tang (1989) developed a two-sided screening procedure using several correlated variables. Tang (1987) and Moskowitz et al. (1991) propos ed some screening models based on economic arguments. Moskowitz et al. (1993) applied a multistage model for the detection of hypertension.
In order to eliminate the undesirable characteristics of overselection and as the uncontrollably high IME inherent in the procedure of Owen et al. (1975), Tsai and Moskowitz (1986) proposed a one-sided Single Screening Procedure (SSP) based on the IME concept. Moskowitz and Tsai (1988) extended the SSP to a Double Screening Procedure (DSP) using two screening variables. Lu (1988) developed software to calculate all results when there are multiple screening variables allocated into two inspection stages. A detailed review of screening procedure has been given by Tang and Tang (1994). The sequential screening procedure proposed in this paper is extending the DSP to a Sequential Screening Procedure (SQSP).
3. Sequential screening procedure
A Sequential Screening Procedure (SQSP) allocating k screening variables into r inspection stages is considered. Let [X.sub.1],..., [X.sub.k] be k screening variables correlated with the performance variable Y with their inspection costs being given by [c.sub.l],..., [c.sub.k]. Without loss of generality, we assume that the performance variable and k screening variables have a multivariate normal distribution with a zero mean vector and a covariance matrix of
[MATHEMATICAL EXPRESSION NOT REPRODUIBLE IN ASCII]
As to the SQSP with r stages, let
[U.sub.1] = [summation over ([i.sub.1][member of][A.sub.1])] [[alpha].sub.[i.sub.1]][X.sub.[i.sub.1]],
[U.sub.2] = [summation over ([i.sub.2][member...
NOTE: All illustrations and photos
have been removed from this article.
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