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The quality loss function developed by Dr. Genichi Taguchi considers three cases including nominal-the-best, smaller-the-better, and larger-the-better. The methodology used to deal with the larger-the-better case is slightly different from that for the smaller-the-better and nominal-the-better cases. This paper attempts to bring about similarity among the three cases by introducing a term called the “target-mean ratio” and proposing a common formula for all three cases. The “target-mean ratio” can take different values to represent all three cases to bring about consistency and simplify the model. Also, it eliminates the assumption of target performance at infinite level and brings the model closer to reality. Characteristics such as efficiency, coefficient of performance (COP), and percent nondefective are presently not larger-the-better characteristics due to the assumption of target performance at infinity and the subsequent necessary derivation of the formulae.

The Mahalanobis Taguchi System is a diagnosis and forecasting method for multivariate data. Mahalanobis distance is a measure based on correlations between the variables and different patterns that can be identified and analyzed with respect to a base or reference group. The issue of multicollinearity is not adequately addressed in the MTS method. In cases where strong relationships exist between variables, the correlation matrix becomes almost singular and the inverse matrix is not accurate. Multicollinearity can be handled by utilizing the adjoint matrix of the correlation matrix and Gram-Schmidt orthogonalization. This paper presents a case study of the MTS methodology with the application of the adjoint matrix to avoid some effects of multicollinearity.