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In product or process parameter design, the case of multiple performance characteristics appears more commonly than that of a single characteristic. Numerous methods have been developed to deal with such multi-characteristic parameter design (MCPD) problems. Among these, this paper considers three representative methods, which are respectively based on the desirability function (DF), grey relational analysis (GRA), and principal component analysis (PCA). These three methods are then used to solve the MCPD problems in ten case studies reported in the literature. The performance of each method is evaluated for various combinations of its algorithmic parameters and alternatives. Relative performances of the three methods are then compared in terms of the significance of a design parameter and the overall performance value corresponding to the compromise optimal design condition identified by each method. Although no method is significantly inferior to others for the data sets considered, the GRA-based and PCA-based methods perform slightly better than the DF-based method. Besides, for the PCAbased method, the compromise optimal design condition depends much on which alternative is adopted while, for the GRA-based method, it is almost independent of the algorithmic parameter, and therefore, the difficulty involved in selecting an appropriate algorithmic parameter value can be alleviated. †

The Taguchi robust design method traditionally deals with single-characteristic problems. Various methods have been developed for extending the Taguchi single-characteristic robust design method to the case of multi-characteristic robust design problems. However, most of those methods have shortcomings in that they do not properly consider the variance-covariance structures among performance characteristics and/or do not preserve the original properties of the Taguchi signal-to-noise ratio for single-characteristic robust design problems. To overcome these shortcomings, this paper develops a multivariate loss function approach to multi-characteristic robust design problems with an appropriately defined signal-to-noise ratio. Its performance is evaluated using simulated examples, and the results indicate that it generally outperforms existing representative methods for correlated as well as uncorrelated experimental data. IntroductionO ne of the most important goals for engineers is to design high-quality products and processes at low cost and within an affordable amount of time. The robust design (or parameter design) method proposed by Taguchi has been widely used as an efficient way of achieving this goal. The purpose of Taguchi robust design is to determine optimal settings of product or process design parameters while making performance characteristics (PCs) robust to uncontrollable noise variables. In the Taguchi robust design method, orthogonal arrays are used for experimental design, and a performance measure (PM) called the signal-tonoise (SN) ratio is calculated at each experimental run. Then, optimal settings of design parameters are determined such that the SN ratio is maximized.The Taguchi robust design method has mainly focused on the case of a single PC although the case of multiple PCs appears more commonly in practice. For example, in the literature, in order to find the optimal settings of the injection-molding parameters to minimize the imbalance of a plastic wheel cover component, two correlated characteristics of the wheel cover component were considered: total weight and the balance of the component. In another example to improve a plasma-enhanced chemical vapor deposition process in the fabrication of integrated circuits, two correlated characteristics of the deposition thickness and a refractive index were considered. Refer to Chiao and Hamada 1 for more details on these examples. A difficulty involved in multi-characteristic robust design (MCRD) is that optimal settings of design parameters may be different from characteristic to characteristic. An important issue in MCRD is how to resolve such conflicts to provide a compromised design condition.Many authors have extended the Taguchi robust design method to the case of MCRD problems. One popular approach is to combine the PMs of PCs into a single aggregated PM and, thereby, re-formulate the MCRD problem as a single-characteristic robust design (SCRD) problem to be solved. For example, the SN ratio for each PC is calculated independently of...