When designing the parameter on the multiple quality characteristics, there has been a study for optimization of problems, but there has been few former study on the possible conflicting phenomena in consideration of the correlations among the characteristics. To solve the issue on the optimal design for multiple quality characteristics, this study modelled the expected loss function with cross-product terms among the characteristics and derived range of the coefficients of the terms. The model will be used to determine the global optimal design parameters where there exists the conflict among the characteristics, which shows difference in optimal design parameters for the individual characteristics.