Quality Loss Function for Bivariate Response – Unified Methodology

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. © 2011 Inderscience Enterprises Ltd.

Department(s)

Engineering Management and Systems Engineering

Keywords and Phrases

bivariate-response; larger-the-better characteristic; linear transformation; MQLFs; multi-response quality loss functions; multi-variate normal distribution; reciprocal transformation

International Standard Serial Number (ISSN)

1757-2185; 1757-2177

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Inderscience, All rights reserved.

Publication Date

01 Jan 2011

Link to Full Text

Share

 
COinS