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Implications of Quality Loss Function in Unified Methodology - LTB Case with Target
ISSN: 1946-3979, e-ISSN: 1946-3987
Published April 14, 2008 by SAE International in United States
Citation: Sharma, N., Cudney, E., Drain, D., and Ragsdell, K., "Implications of Quality Loss Function in Unified Methodology - LTB Case with Target," SAE Int. J. Mater. Manf. 1(1):768-777, 2009, https://doi.org/10.4271/2008-01-1435.
Another methodology has been proposed by Sharma and Ragsdell to bring about similarity among the three cases smaller-the-better, nominal-the-best, and larger-the-btter by introducing a term called the “target-mean ratio” and proposing a unified formula for quality loss. The new methodology has some implications that need to be addressed. This paper attempts to study the implications and effects of the new methodology on the field of quality engineering. This paper presents an implied classification of LTB characteristics according to Taguchi on the basis of a target value at infinity and also discusses the classification of LTB characteristics based on the new methodology. A new concept of “Complementary Characteristic” is also suggested. It is suggested that whether a given LTB characteristic or its complementary characteristic is considered for one and the same case, the quality loss must be equal for both the characteristics. It is then shown mathematically that with the use of the new methodology any LTB characteristic and its complementary characteristic have the same mean-squared deviation (MSD) or quality loss when the target is set according to α = 2, or at 100%, or at any other value, without a loss of generality and consistency. In this way, it is argued that the common methodology is better and more suitable for the purpose of computing quality loss. It is also studied and deliberated upon as to what should be the most appropriate value of ‘α,’ the “target-mean ratio”.