Taguchi believes that even if it is a qualified product (the output quality characteristics are within the tolerance range required by users), the fluctuation of its output characteristics can still cause losses to users and society, and the farther the output characteristics are from its target value, the greater the loss. Therefore, the output characteristic should be as close as possible to its target value. Taguchi suggested using the quality loss function to measure the loss caused by the deviation of the output characteristics of qualified products from the target value.

The quality characteristics of products will deviate from the target value under the influence of noise, and different degrees of deviation will cause different degrees of losses to users. Let the measured value of product quality characteristics be y, the target value (or central value) of quality characteristics be m, and the loss when the measured value deviates from the target value is expressed by L(y), then L(y) is a function of deviation (Y-m), which is called loss function. The loss function L(y) is expanded into Taylor series near m.

When y=m, it will obviously not bring losses to users, so the first term L(m)=0. Since L(Y) has a minimum value when Y=M, the derivative is obtained.