INTRODUCTION

A statistical technique, Mahalanobis distance (MD), is used to distinguish one group from another considering different characteristics of a multidimensional system. The multidimensional system could be a health examination system, a university student's admission system, a printed circuit board inspection system or a sensor system. When an MD is calculated it takes care of the correlation among the characteristics of the multidimensional system. Dr. Genichi Taguchi's latest research is associated with developing robust multidimensional systems by using the Mahalanobis distance. A famous Indian statistician, P.C. Mahalanobis, the founder of the Indian Statistical Institute, introduced MD. In Japan, this method of optimization is becoming popular as the Mahalanobis Taguchi System (MTS). There are several case studies in Japan that have demonstrated the usefulness of this method.

In quality engineering terminology, diagnosis is measurement. There are two values required in a measurement system: a base point and unit. A base point of a weighing scale is the zero point when no weight is on the scale. The unit could be a pound or a kilogram. In diagnosis applications, first we need to construct the base point (Mahalanobis space) from normal conditions. This is used as a reference point. The characteristics of multidimensional systems are compared using this reference point. If an MD corresponding to a set of characteristics is very close to MDs corresponding to the normal population, that set would be considered part of the normal population otherwise, it is considered abnormal.

The signal-to-noise (S/N) ratio is used...