Principal component analysis (PCA)-based approaches for the multi-response optimisation: an issue and the recommendation

One weakness in Taguchi method is that it focuses on optimisation of single response variable only whereas most of the modern manufacturing processes demand for simultaneous optimisation of multiple responses, and some of these responses are often correlated. Recently some principal component analysis (PCA)-based approaches have been proposed in literature which aims at making the Taguchi method useful for optimising correlated multiple responses too. The implicit assumption made in these procedures is that the correlations among the response variables can be taken care by taking into account the correlations among the signal-to-noise ratios of the response variables. This article shows that this assumption may not be true always. Therefore, some corrections are proposed in the computational procedures of PCA-based approaches, which are described taking into consideration weighted principal component and PCA-based grey relational analysis methods. The results of analysis of two sets of past experimental data indicate that the corrected PCA-based approaches result in substantial improvement in the overall optimisation performance.