Multi-response optimization using principal component analysis and grey relational analysis

Taguchi's method is a highly effective means of improving product/process quality for extensive industrial applications. More than one quality characteristic must be simultaneously considered to evaluate the product quality in light of the increasing complexity of product designs. Most Taguchi method practitioners employ engineering judgment to determine the final optimal factor/level combination when several responses are to be optimized. However, this approach is very subjective and always brings some uncertainty to the decision-making process. Furthermore, moderate or strong correlations among multiple responses always exist and these correlations may create serious conflicts when determining the optimal factor/level combination. Additionally, the relative importance among responses must also be considered when employing Taguchi's method to simultaneously optimize multiple responses. This study presents an alternative approach based on Principal Component Analysis (PCA) and Grey Relational Analysis (GRA) to determine an Overall Quality Performance Index (OQPI) for multiple responses. A case study that optimizes the chemical-mechanical polishing of copper (Cu-CMP) thin films from an integrated circuit manufacturer in Taiwan demonstrates the effectiveness of the proposed procedure.