| Abstract: | Consider a situation in which the items produced by a production process are sorted into two grades according to predetermined specifications and sold at two different prices. A loss is incurred by the producer when an item is classified into a grade and its quality does not meet the consumer's requirement of that grade. A loss in selling price is also incurred when an item is classified into a lower quality grade when it can meet the consumer's requirement of a higher grade. Consequently, the producer's profit is determined by sale prices and losses due to consumer dissatisfaction. The optimal grading specifications are determined to maximize the expected profit. Design of product grading procedures can be based on the performance variable of interest or a surrogate variable correlated with the performance variable. The practice of using correlated variables in product grading is common in industry. We develop product grading models for both the performance variable and a correlated variable. |
