Quality Utility—A Compromise Programming Approach to Robust Design

TLDR

Robust design typically balances mean performance and variability, but existing methods such as Taguchi’s signal‑to‑noise ratio or weighted‑sum approaches are insufficient. This study proposes a utility‑based bi‑objective robust design framework that leverages compromise programming. A preference‑structured procedure uses the Tchebycheff compromise programming method, with a quadratic utility equivalent to a weighted Tchebycheff metric, to identify Pareto‑efficient robust designs. The resulting utility function enables local exploration of efficient solutions and the iterative procedure facilitates decision‑making in quality engineering and robust design applications.

Abstract

In robust design, associated with each quality characteristic, the design objective often involves multiple aspects such as “bringing the mean of performance on target” and “minimizing the variations.” Current ways of handling these multiple aspects using either the Taguchi’s signal-to-noise ratio or the weighted-sum method are not adequate. In this paper, we solve bi-objective robust design problems from a utility perspective by following upon the recent developments on relating utility function optimization to a Compromise Programming (CP) method. A robust design procedure is developed to allow a designer to express his/her preference structure of multiple aspects of robust design. The CP approach, i.e., the Tchebycheff method, is then used to determine the robust design solution which is guaranteed to belong to the set of efficient solutions (Pareto points). The quality utility at the candidate solution is represented by means of a quadratic function in a certain sense equivalent to the weighted Tchebycheff metric. The obtained utility function can be used to explore the set of efficient solutions in a neighborhood of the candidate solution. The iterative nature of our proposed procedure will assist decision making in quality engineering and the applications of robust design.