Quality Loss Function – A Common Methodology for Three Cases

Document Type : Research Paper


The quality loss function developed by Genichi Taguchi considers three cases, nominal-thebest, smaller-the-better, and larger-the-better. The methodology used to deal with the larger-thebetter case is slightly different than the other two cases. This research employs a term called target-mean ratio to propose a common formula for all three cases to bring about similarity among them. The target-mean ratio can take different values representing all three cases to bring consistency and simplicity in the model. In addition, it eliminates the assumption of target performance at an infinite level and brings the model closer to reality. Characteristics such as efficiency, coefficient of performance, and percent non-defective are presently not larger-thebetter characteristics due to the assumption of target performance at infinity and the subsequent necessary derivation of the formulae. These characteristics can also be brought under the category of the larger-the-better characteristics. An example of the efficiency of prime movers is discussed to illustrate that the efficiency can also be considered as a larger-the-better characteristic. A second example is presented to suggest the subtle differences between both methodologies.


Main Subjects

[1] Ferreira O.C., http://ecen.com/content/eee7/motoref.htm, April 2005.
[2] Fowlkes W.Y., Creveling C.M. (1995), Engineering methods for robust product design; Addison-
[3] Maghsoodloo S. (1991), The exact relationship of Taguchi's signal-to noise ratio to his quality loss
function; Journal of Quality Technology 22(1); 57-67.
[4] Phadke M. S. (1989), Quality engineering using robust design; Prentice-Hall, Englewood Cliffs, New
[5] Taguchi G., Chowdhury S., Taguchi S. (1999), Robust engineering; McGraw-Hill.
[6] Taguchi G., Chowdhury S., Wu Y. (2004), Taguchi’s quality engineering handbook; Edition 2004, pp.
[7] Taguchi G., Elsayed A., Hsiang T. (1989), Quality engineering in production systems; McGraw-Hill
Publishing Company.
[8] Venkateswaren S. (2003), Warranty cost prediction using Mahalanobis Distance, MS Thesis,
University of Missouri-Rolla.