Performance Measures of Products with Multiple Characteristics Utilizing Unit Costs of Nonconformance

Abstract

A majority of products for manufacturing or consumers have multiple characteristics that must meet the requirements of the customer. For example, a steel beam any have dimensional tolerances on its length, width, or height and functional tolerances on its strength. The characteristics are influenced by different processes that create the product. For an individual characteristic, process capability measures exist that convey the degree to which the characteristic meets the specification requirements. Such measures may indicate the proportion of nonconforming product related to the particular characteristic, under some distributional assumptions of the characteristic. For products with multiple characteristics, the unit costs of rectification may be different, making the satisfaction of some characteristics meeting customer requirements more important than others. In this paper, an aggregate process capability performance measure is developed that considers the relative importance of the characteristic based on unit costs of nonconformance. Based on the aggregate measure, appropriate process capability measures for the individual measures are also derived. Bounds on the aggregate capability measures are also established.