Simultaneous Optimization of Correlated Multiple Surface Quality Characteristics of Mild Steel Turned Product

Abstract

Present work highlights application of utility theory combined with Principal Component Analysis (PCA) and Taguchi’s robust design for simultaneous optimization of correlated multiple surface quality characteristics of mild steel machined product prepared by straight turning operation. The study aims at evaluating the most favorable process environment followed by an optimal parametric combination for achieving high surface quality. Traditional Taguchi based hybrid optimization approaches rely on the assumption that quality indices are uncorrelated or independent. But it is felt that, in practice, there may be some correlation among various quality indices (responses) under consideration. To overcome this limitation of Taguchi approach, the present study proposes application of PCA to convert correlated responses into uncorrelated quality indices called principal components. Finally based on utility theory, Taguchi method has been applied to solve this optimization problem. The study demonstrates detailed methodology and concludes robustness and flexibility of the proposed optimization technique and validates its effectiveness through a case study in which correlated multiple response characteristics of turning operation have been optimized

A modified principal component analysis-based utility theory approach for optimization of correlated responses of EDM process

“…However, none of the above methods for multi-response optimization takes into account the possible correlations between the responses that may exist. In order to take care of the possible correlations between the response variables, many researchers (Tong and Wang, 2002;Tong et al, 2005;Liao, 2006;Datta and Mahapatra, 2010) proposed to make use of PCA (Johnson and Wichern, 1996). The PCA technique can transform several related variables into a smaller number of uncorrelated principal components, which are linear combinations of the original variables.…”

“…Tong and Wang (2002) proposed PCA-based GRA method, Wu and Chyu (2004) suggested PCA-based PQLR method, Tong et al (2005) presented PCA-based TOPSIS method and Liao (2006) proposed weighted principal component (WPC) method. Recently, Datta and Mahapatra (2010) proposed the PCA-based UT approach to optimize multiple responses that may be correlated. The PCA-based UT approach seems to be very appealing.…”

“…So the amount of deviations of different response variables from their ideal values can be estimated for different trials. Datta and Mahapatra (2010) called these deviations as quality losses (Taguchi's definition for quality loss is different). The quality losses can be appropriately converted into preference numbers and overall utility values, using Eqns.…”

“…This approach should work well if the response variables are independent. Datta and Mahapatra (2010) observed that the response variables might not be always independent. Therefore, they proposed to estimate the quality losses with respect to principal component scores (i.e.…”

A multivariate quality loss function approach for parametric optimization of non-traditional machining processes

“…MRR, percentage improvement of surface finish and scatter of SR in a centrifugal force-assisted abrasive flow machining process. Datta and Mahapatra (2010) combined utility theory with principal component analysis and Taguchi robust design for simultaneous optimization of multiple correlated surface quality characteristics of mild steel in straight turning operation. Dave et al (2012) proposed the application Taguchi loss function as a multi-response optimization tool for electro discharge machining (EDM) operation of Inconel 718 alloy.…”