This paper considers the problem of determining the optimum target values of the quality characteristic of interest Y and the screening limits of a surrogate variable X which is correlated with Y under two-stage screening procedure. In the two-stage screening procedure, X is measured first to decide whether an item should be accepted, rejected or additional observations should be taken. If it is difficult to decide on the result of measured value of X, Y is then observed to classify the undecided items. Assuming that Y and X are jointly normally distributed, a model is constructed which involves selling and reduced prices, production, inspection, and penalty costs. Methods of finding the optimum process mean and the screening limits are presented. A numerical example and analysis of the results are also presented.