A Review and Analysis of the Mahalanobis—Taguchi System

Abstract

The Mahalanobis–Taguchi system (MTS) is a relatively new collection of methods proposed for diagnosis and forecasting using multivariate data. The primary proponent of the MTS is Genichi Taguchi, who is very well known for his controversial ideas and methods for using designed experiments. The MTS results in a Mahalanobis distance scale used to measure the level of abnormality of “abnormal” items compared to a group of “normal” items. First, it must be demonstrated that a Mahalanobis distance measure based on all available variables on the items is able to separate the abnormal items from the normal items. If this is the case, then orthogonal arrays and signal-to-noise ratios are used to select an “optimal” combination of variables for calculating the Mahalanobis distances. Optimality is defined in terms of the ability of the Mahalanobis distance scale to match a prespecified or estimated scale that measures the severity of the abnormalities. In this expository article, we review the methods of the MTS and use a case study based on medical data to illustrate them. We identify some conceptual, operational, and technical issues with the MTS that lead us to advise against its use.

KEY WORDS:

• Classification analysis
• Discriminant analysis
• Medical diagnosis
• Multivariate analysis
• Pattern recognition
• Signal-to-noise ratio
• Taguchi methods