Design of a two‐stage screening procedure using correlated variables: A loss function approach

Because of the rapid growth in automated manufacturing systems, complete inspection (screening) becomes very attractive. Sophisticated automated inspection equipment can efficiently process a large number of items and produce consistent and accurate results. However, in many applications the performance variable of interest is expensive to measure even by using automated inspection equipment. One alternative to deal with this problem is to use another variable, which is correlated with the performance variable and relatively inexpensive to measure as the screening variable. Since a screening variable is not perfectly correlated with the performance variable, decision errors that reject good‐quality items or accept poor‐quality items may occur. To reduce these errors, we propose a two‐stage screening procedure in which the first‐stage screening is based on a screening variable and the second‐stage screening is based on the performance variable. The second‐stage screening is performed only on those items of which the disposition cannot clearly be determined by the result of first stage screening. Three losses are considered in the formulation of the model. The first loss is the cost of inspection, the second loss is the cost associated with the disposition of rejected items, and the third loss is incurred by imperfect quality of accepted items. The optimal solution is derived and compared to the single‐stage screening procedures based on the screening variable and the performance variable. In addition, the sensitivity of the optimal screening procedure with respect to the correlation between the performance variable and the screening variable and the cost of inspecting the performance variable is discussed and demonstrated by numerical results.