Optimization of multiple responses using principal component analysis and technique for order preference by similarity to ideal solution

Optimizing multi-response problems has become an increasingly relevant issue when more than one correlated product quality characteristic must be assessed simultaneously in a complicated manufacturing process. This study proposes a novel optimization procedure for multiple responses based on Taguchi's parameter design. The signal-to-noise (SN) ratio is initially used to assess the performance of each response. Principal component analysis (PCA) is then conducted on the SN values to obtain a set of uncorrelated components. The optimization direction for each component is determined based on the corresponding variation mode chart. Finally, the relative closeness to the ideal solution resulting from the technique for order preference by similarity to ideal solution (TOPSIS) is determined as an overall performance index (OPI) for multiple responses. Engineers can easily employ the proposed procedure to obtain the optimal factor/level combination for multiple responses. A case study involving optimization of the chemical-mechanical polishing of copper (Cu-CMP) thin films from an integrated circuit manufacturer in Taiwan is also presented to demonstrate the effectiveness of the proposed procedure.