Mathematical backgrounds for Quality Engineering

2. Orthogonal expansion

Abstract

A quadratic form expansion is the base of calculating S/N ratios as the measures of functionality. It is not easy to check orthogonality among quadratic forms having degree of freedom, or rank, more than 1. The methods to decompose a quadratic form having degree of freedom more than one into the ones having degree of freedom one are introduced in this article. A quadratti form having degree of freedom one is obtained from linear form of data and it is easy to ch㏄k orthogonality among linear forms.