Mahalanobis Taguchi system: a review

Abstract

Purpose – The purpose of this paper is to present and analyze the current literature related to developing and improving the Mahalanobis-Taguchi system (MTS) and to present the shortcomings related to this method for future research. Design/methodology/approach – In this paper, articles in the literature are classified to give an overview on the MT strategy. For this purpose, 46 articles are considered for classification from 2000 to 2013 on the basis of: MTS contribution area, description of the issue, and results. Findings – In this paper a review on the concepts and operations of the MTS was provided as a new method in the field of pattern recognition, multivariable diagnosis, and forecasting. A large number of studies were performed in recent years consisting of developing MTS and MTS case studies. The analysis of the articles showed the fields of MTS which had more potential for future studies and developing. The comparison of the MTS to other methods and the selection of the normal group for constructing the Mahalanobis space have received the most attention by researchers. In addition, several studies concentrated on the use of other methods instead of design of experiments, finding applications for multiclass MTS and finding an alternative for the SN ratio. Originality/value – This paper contains the publications in the field of MTS chronologically and shows different areas for developing and case studies. It will be useful to researchers and professionals who are interested in pattern recognition, multivariate analysis, and forecasting.

Improved method for correcting sample Mahalanobis distance without estimating population eigenvalues or eigenvectors of covariance matrix

“…The detailed procedure of the Monte Carlo simulation is shown in "Appendix B.1". Furthermore, the dependence on the population eigenvalues λ i should be considered because the correcting methods of fSd (37), Ld (38), and fLd (39) derived from (6) and (8) are based on the assumption that…”

“…As n → ∞, l i converges to λ i according to (6) and (7) in probability, and f i also converges to φ i according to (8) in probability. Therefore, T 2 converges to D 2 as n → ∞.…”

“…The MD can be easily defined using the covariance matrix of learning samples and can be calculated faster and more easily than neural networks (NNs) and support vector machines (SVMs). The MD is still widely used for industrial and various other purposes (see a recent example [3]), and there have been cases in which the MD was said to have better recognition performance than NNs and SVMs if there are few learning samples [4][5][6][7]. Usually, the population covariance matrix Σ of the learning samples is unknown in advance.…”

Selección óptima de variables mediante metaheurísticas binarias para la detección de fallas en un proceso industrial multivariado usando aprendizaje de máquina

“…donde f 1 (x) es una función que mide el error en la clasificación binaria de los datos, mientras p seleccionadas es el subconjunto de variables seleccionado. Siguiendo el enfoque de la metodología llamada sistema Mahalanobis-Taguchi (MTS) [6]. La distancia Mahalanobis es utilizada con el fin de clasificar los datos en dos clases, conocidas como datos saludables y no saludables.…”

Applying the Mahalanobis–Taguchi System to Improve Tablet PC Production Processes

“…Therefore, the increases in SN ratio before and after analysis can be analyzed to assess improvements in system functioning. Finally, validation group data were used for testing to confirm whether the reduced model exhibited sufficient classification and diagnostic capabilities [26][27][28][29][30].…”