Signal-to-Noise ratio and design complexity based on Unified Loss Function – LTB case with Finite Target

Abstract

Taguchi’s quality loss function for larger-the-better performance characteristics uses a reciprocal transformation to compute quality loss. This paper suggests that reciprocal transformation unnecessarily complicates and may distort results. Examples of this distortion include the signal-to-noise ratio based on mean squared deviation and the signal-to-noise ratio based on complexity. The concept of complexity is an important element of axiomatic design and axiomatic quality. This paper shows that a simple linear transformation as used in the unified loss function can give an appropriate and comparable signal-to-noise ratio based on mean squared deviation and signal-to-noise ratio based on complexity for larger-the-better characteristics. Mathematical derivations are given and two examples are discussed to demonstrate the proposed methodology.