Quadratic loss functions and signal-to-noise ratios for a bivariate response

Abstract

Abstract In this paper, the quadratic quality loss functions and signal-to-noise (S/N) ratios for a bivariate response are developed. Quality characteristics by variables are divided into three types: (1) Smaller the better (STB), (2) Larger the better (LTB), and (3) Nominal the best (NTB). The focus is on the bivariate quality characteristic response combinations (NTB, NTB), (STB, STB), and (LTB, LTB) cases. The treatment of mixed bivariate (STB, LTB), (STB, NTB), and (LTB, NTB) response cases will be forthcoming as a sequel to this paper in the next issue of this journal (Vol. 20, No. 2, 2001). The relationships among quality loss constants are also discussed in each case. An example of a robust parameter design experiment using simulated data is provided to illustrate the use of signal-to-noise ratios, which were developed to identify the optimal factor settings. The design matrix used in the example was an L 8 (2 7 ) Taguchi orthogonal array (OA) as a one-half fraction of a 2 4 full factorial experiment.