A feasibility study in adapting Shamos Bickel and Hodges Lehman estimator into T-Method for normalization

4th Asia Pacific Conference on Manufacturing Systems; 3rd International Manufacturing Engineering Conference

Harudin, N.^1,2 ; Jamaludin, K.R.^1 ; Nabil Muhtazaruddin, M.^1 ; Ramlie, F.^1 ; Muhamad, Wan Zuki Azman Wan^1

Razak School in Engineering and Advanced Technology, Universiti Teknologi Malaysia, Kuala Lumpur

54100, Malaysia^1

Department of Mechanical Engineering, Universiti Tenaga Nasional, Kajang Selangor

43000, Malaysia^2

关键词: Classical methods;    Classical statistics;    Error percentage;    Feasibility studies;    Mahalanobis-taguchi systems;    Mean and standard deviations;    Multivariate data;    Robust parameters;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/319/1/012033/pdf
DOI  :  10.1088/1757-899X/319/1/012033

来源: IOP

【 摘 要 】

T-Method is one of the techniques governed under Mahalanobis Taguchi System that developed specifically for multivariate data predictions. Prediction using T-Method is always possible even with very limited sample size. The user of T-Method required to clearly understanding the population data trend since this method is not considering the effect of outliers within it. Outliers may cause apparent non-normality and the entire classical methods breakdown. There exist robust parameter estimate that provide satisfactory results when the data contain outliers, as well as when the data are free of them. The robust parameter estimates of location and scale measure called Shamos Bickel (SB) and Hodges Lehman (HL) which are used as a comparable method to calculate the mean and standard deviation of classical statistic is part of it. Embedding these into T-Method normalize stage feasibly help in enhancing the accuracy of the T-Method as well as analysing the robustness of T-method itself. However, the result of higher sample size case study shows that T-method is having lowest average error percentages (3.09%) on data with extreme outliers. HL and SB is having lowest error percentages (4.67%) for data without extreme outliers with minimum error differences compared to T-Method. The error percentages prediction trend is vice versa for lower sample size case study. The result shows that with minimum sample size, which outliers always be at low risk, T-Method is much better on that, while higher sample size with extreme outliers, T-Method as well show better prediction compared to others. For the case studies conducted in this research, it shows that normalization of T-Method is showing satisfactory results and it is not feasible to adapt HL and SB or normal mean and standard deviation into it since it's only provide minimum effect of percentages errors. Normalization using T-method is still considered having lower risk towards outlier's effect.