There are various definition about quality.

Many people have defined the quality.

But most of all are abstract and difficult to measure.

Dr.Taguchi defined "The quality is the loss of society after the products shipment. The loss does not included from its poor function."

He proposed the quality is loss amount.

Taguchi's loss function

The loss is increase in proportion to square of the diffference from the target.

This definition makes statistical value, standard deviation and variation, is meaningful information.

Loss amount : L=A/⊿*(x-m)^2

A: Loss on functional limit, ⊿:functional limit, m:target value,  x: value

This formula is approximation.

Idea of square is come from Taylor expansion.

S/N ratio is also based on this formula.

W.Edwards Deming from "Out of the crisis" p.141

"A better description of the world is Taguchi loss function in which there is minimum loss at the nominal value, and an ever-increasing loss with  departure either way from the nominal value."