Quality loss function for bivariate response – unified methodology. (14th July 2011) - Sharma, Naresh K.; Cudney, Elizabeth A.
Various methods have been proposed for multi-response quality loss functions as an extension of the quality loss function for a single characteristic given by Taguchi. Multivariate responses are assumed to follow a multivariate normal distribution. When one of the characteristics is transformed using a reciprocal transformation the characteristic itself and the multivariate response do not remain normally distributed. In these circumstances, the basic assumption of a multivariate normal distribution does not hold. Moreover, the reciprocal transformation has several issues such as inconsistency in the methodologies among the three characteristics, incomparable results, and inappropriate change of parameter unit. The multi-response quality loss function also requires the reciprocal transformation for larger-the-better characteristics. This paper proposes a simple linear transformation for a bivariate response which combines the larger-the-better characteristic with any of the characteristics. This enables all three types of characteristics to use one type of transformation to achieve more appropriate results; i.e., linear transformation. Two examples of bivariate case are also discussed to demonstrate the methodology.