Multi-response optimization using weighted principal component

Abstract

Taguchi method is a very popular offline quality design. However, it cannot solve the multi-response problem which occurs often in today's society. Research shows that the multiresponse problem is still an issue with the Taguchi method. Researchers have tried to find a series of theories and methods in seeking a combination of factors/levels to achieve the situation of optimal multi-response instead of using engineers' judgement to make a decision in the Taguchi method. In 1997, Su et al. submitted the multivariate method, and in 2000 Antony proposed principal component analysis (PCA), to solve this problem. But with the PCA method, there are still two main shortcomings. In this study, the weighted principal components (WPC) method is proposed to overcome these two shortcomings, and three cases in their papers will be illustrated and compared in the application of WPC method. The result shows that the WPC method offers significant improvements in quality.

Multi-objective optimization of cutting parameters in high-speed milling based on grey relational analysis coupled with principal component analysis

“…Principal component analysis (PCA) is a useful statistical method to convert multi-indicators to several compositive ones [14,15]. In multivariate studies, the information of observations overlaps due to many variables and their internal correlation to some extent.…”

Selection of a suitable multiresponse optimization technique for turning operation

“…The depth of cut was found to have most impact on the average roughness and the cutting speed was the most influential factor for the roughness and the roundness. Liao (2006) proposed a weighted principal component (WPC) analysis method, which took into account the possible correlations among various responses. Rao et al (2013) adopted Taguchi's technique to study the influence of speed, feed and depth of cut on cutting force and surface roughness in turning AISI 1050 steel using ceramic tool.…”

“…MRSN ratio method (Nian et al, 1999), WSN ratio method (Shiau, 1990;Tai et al, 1992), GRA method (Lin et al, 2009), and VIKOR method (Tong et al, 2007) are quite simpler/robust in accordance to their computational procedures. There are some other multiresponse optimization techniques (Sahin & Motorcu, 2008;Sardinas et al, 2006;Jeyapaul et al, 2006;Liao, 2006), which use complex mathematical/statistical tools and are, therefore, inconvenient to be used by the industrial personnel with little background in statistics and knowledge of software. Because of the computational simplicity, the above four multi response optimization techniques are chosen for the current study.…”

Optimization of Correlated Multiple Response Surfaces with Stochastic Covariate

“…Second, the total variance in the data does not count in the optimization process of the mentioned methods. In order to overcome these two main shortcomings in these methods, Liao [4] and Wu and Chyu [5] presented methods based on weighted principal components (WPC) as in the former, PCA is conducted on signal to noise ratio values, whereas in the latter, PCA is conducted on a proportion of quality loss reduction values. In WPC method, all components are considered in order to completely explain variation in all responses.…”