# History of Dynamic SN Ratio

The types of dynamic characteristics of quality engineering are best organized in the Classification of Characteristics, and the corresponding signal-to-noise ratio is I think that the one on Dynamic SN Ratio page is appropriate.

On the other hand, the conventional literature gives a different explanation.

## Types of dynamic characteristics

There are three types of dynamic characteristics that can be explained: the zero-point proportional formula, the reference point proportional formula, and the first-order equation.

Compared to Classification of Characteristics page, the following correspondence is available.

### Relationship between equal and proportional variance

In the conventional literature, the words "equal variance and proportional variance" do not appear. Proportional variance is explained as "there is a point where it is clear that the output will be zero", and it is conscious that there are two types of phenomena expressed in linear form.

The correspondence between the conventional classification of literature and "equal and proportional dispersion" is as follows. However, in the conventional explanation, it seems that it does not go beyond the fact that "there is a point where it is clear that the output will be 0". Therefore, although it is not shown what the distribution will be, I think that the following correspondence is roughly correct.

• Zero-point proportionality formula and reference point proportionality formula : proportional variance
• First-order equation : equal variance

The difference between the zero-point proportionality formula and the reference point proportionality formula is as follows.

• Zero-point proportionality formula : The zero point (origin) is the point of zero variation.
• Reference point proportionality formula : Anything other than the zero point (origin) is a point with zero variation.

### Consideration of phenomena proportional to inclination

As far as I know, The phenomenon that "data that requires a linear form may have different variations depending on the input" has been divided into proportional type and first-order expression type. This perspective is looking at whether it is proportional to X or not.

The fact that it is also proportional to the slope is included in the structure of the signal-to-noise ratio in the form of "dividing the slope by the error variance".

However, it is doubtful that it is acceptable to assume that the variation is proportional to the slope for any phenomenon. If you are going to prepare a signal-to-noise ratio by distinguishing between equal variance and proportional variance, I think it is better to prepare a signal-to-noise ratio by distinguishing between cases that are proportional to the slope and those that are not. Therefore, the author has included the case where it is proportional to the slope and the case where it is not, as a distinction between characteristics.

## Proper use of SN ratio

### In the case of relatively old literature

In relatively old literature, dynamic characteristics are divided into three types. The reference point proportional formula is adjusted to be the zero point. Adjust the first-order equation so that it passes through the origin.

The signal-to-noise ratio used after adjustment is the same.

### In the case of relatively new literature

In the relatively new literature, the SN ratio of Energy ratio type and fluctuation ratio type appears.

Among them, there is an explanation of the difference between the SN ratio before the advent of the energy ratio type and the fluctuation ratio type, but the perspective of "proper use" has been put forward.

The key to using it properly is the difference between equal and proportional distribution. On this site, I wrote it in a way that centered on that point.