Title: Quality loss function for bivariate response – unified methodology

Authors: Naresh K. Sharma, Elizabeth A. Cudney

Addresses: Engineering Management and Systems Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA. ' Engineering Management and Systems Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA

Abstract: 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.

Keywords: bivariate response; larger-the-better characteristic; linear transformation; multivariate normal distribution; multiresponse quality loss functions; MQLFs; reciprocal transformation.

DOI: 10.1504/IJQET.2011.041229

International Journal of Quality Engineering and Technology, 2011 Vol.2 No.3, pp.229 - 253

Available online: 13 Jul 2011 *

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