Directional Mahalanobis Distance and Parameter Sensitivities
Mahalanobis Distance (MD) is gaining momentum in many fields where classification, statistical pattern recognition, and forecasting are primary focus. It is a multivariate method and considers correlation relationships among parameters for computing generalized distance measure to separate groups or populations. MD is a useful statistic in multivariate analysis to test that an observed random sample is from a multivariate normal distribution. This capability alone enables engineers to determine if an observed sample is an outlier (defect) that falls outside the constructed (good) multivariate normal distribution. In Mahalanobis-Taguchi System (MTS), MD is suitably scaled and used as a measure of severity in abnormality assessment. It is obvious that computed MD depends on values of parameters observed on a random sample. All parameters may not equally impact MD. MD could be highly sensitive with respect to some parameters and less sensitive to some other parameters.