Relationship with SN Ratio - Larger-the-better Characteristics with Finite Target

The concept of complexity is an essential constituent of axiomatic design and axiomatic quality. A reciprocal transformation is used to compute quality loss for larger-the-better performance characteristics in Taguchi’s methodology. El-Haik’s work on connecting robust design and axiomatic design with the help of mathematical relationships also considers the reciprocal methodology for larger-the-better functional requirements. Because of reciprocal transformation axiomatic complexity formulation for larger-the-better performance characteristics is different from that for smaller-the-better and nominal-the-best characteristics. Second, the signal-to-noise ratio based on complexity is also different for the same reason. This paper shows that a simple linear transformation in which a finite target is assumed can give more appropriate and comparable signal-to-noise ratio based on complexity for larger-the-better characteristics. Mathematical relationships are given and an example is employed to demonstrate the proposed methodology.