Increasing T-Method Accuracy Through Application of Robust M-Estimatior

Abstract

Mahalanobis Taguchi System is an analytical tool involving classification, clustering as well as prediction techniques. T-Method which is part of it is a multivariate analysis technique designed mainly for prediction and optimization purposes. The good things about T-Method is that prediction is always possible even with limited sample size. In applying T-Method, the analyst is advised to clearly understand the trend and states of the data population since this method is good in dealing with limited sample size data but for higher samples or extremely high samples data it might have more things to ponder. T-Method is not being mentioned robust to the effect of outliers within it, so dealing with high sample data will put the prediction accuracy at risk. By incorporating outliers in overall data analysis, it may contribute to a non-normality state beside the entire classical methods breakdown. Considering the risk towards lower prediction accuracy, it is important to consider the risk of lower accuracy for the individual estimates so that the overall prediction accuracy will be increased. Dealing with that intention, there exist several robust parameters estimates such as M-estimator, that able to give good results even with the data contain or may not contain outliers in it. Generalized inverse regression estimator (GIR) also been used in this research as well as Ordinary Lease Square Method (OLS) as part of comparison study. Embedding these methods into T-Method individual estimates conditionally helps in enhancing the   accuracy of the T-Method while analyzing the robustness of T-method itself.  However, from the 3 main case studies been used within this analysis, it shows that T-Method contributed to a better and acceptable performance with error percentages range 2.5% ~ 22.8% between all cases compared to other methods. M-estimator is proved to be sensitive with data consist of leverage point in x-axis as well as data with limited sample size.   Referring to these 3 case studies only, it can be concluded that robust M-estimator is not feasible to be applied into T-Method as of now. Further enhance analysis is needed to encounter issues such as Airfoil noise case study data which T -method contributed to highest error% prediction.  Hence further analysis need to be done for better result review.