Formulating Effective Performance Measures for Systems with Multiple Quality Characteristics

One of the main objectives in engineering-whether design or manufacturing-is to minimize variations in quality characteristics of a system. The system can either be a product or a process. Minimizing variation requires defining a quantitative measure of variation; in other words a performance measure. Several performance measures have been defined and continue to be utilized primarily to design systems with a single dominant quality characteristic. However, almost every system has more than one quality characteristics considered important by the designer of the process or the consumer of the product. Designing robust systems with multiple-often competing-quality characteristics is difficult for a designer because of the uncertain correlation among the design objectives. It is the purpose of this paper to suggest a method for improving the quality of a system with multiple quality characteristics. The desired properties a performance measure should possess are outlined. Measures such as quality loss, signal-to-noise ratio, information content, and rolled throughput yield are examined and their use extended for systems with multiple quality characteristics. These are also looked at in the context of the desired properties such measures should possess. The concept of differential entropy, as defined in information theory, is presented as a candidate performance measure for both single and multiple quality characteristics systems. The suitability of differential entropy as a measure of variation is then compared to existing measures. A case study is presented which demonstrates the use of performance measures in engineering design.