# Static SN Ratio

SN ratio in Quality Engineering is made as
"Unevenness is small" = "SN ratio is large"
.

• Preferably target characteristics : log ( Square of ( (Ave of Y) / (StDev of Y) ) )
• Zero preferably target characteristics : log ( Square of ( 1 / (Stdev of Y) ) )
• Preferably small characteristics : log ( 1 / ( Ave of Sum of Square of Y ) )
• Preferably large characteristics : log ( 1 / Ave of Inverse of Sum of Square of Y ) )
• Dynamic characteristics : log ( square of ( slope / StDev of Y ) )

Ave = Average
StDev = Standard Deviation

## Supplement to Formulas

In the above, it is not a general way of writing quality engineering textbooks, but a writing style that is easy for people who are familiar with data science to imagine.

### Variations of expressions

In quality engineering practices, In many cases, corrections are made using quantities called Sm and Ve, resulting in a complex structure. This correction method has the problem of not being able to calculate the signal-to-noise ratio. In my experience, the conclusion does not change depending on whether or not there is a correction. It makes it difficult to understand the meaning of the signal-to-noise ratio.

The above formula is summarized by removing the correction term and further transforming it into an easy-to-imagine expression such as "mean value" and "standard deviation".

As an improved version of the signal-to-noise ratio, there is also Energy ratio type and fluctuation ratio type.

### Logarithmic conjugation

In quality engineering practice, the signal-to-noise ratio is expressed as a common logarithm. In addition, the logarithmic value is multiplied by 10. But even if you don't use natural logarithms or multiply by 10, It does not affect the results of the experiment.

However, the logarithmic numbers will be added together at a later stage, and "additiveness" is required to do so, so it does not have to be logarithmic.

Logarithms are even better, which is summarized on the page Assessing differences in variation for small data.

### Ratio data

atio data that can only take values from 0 to 1 is not impossible to handle as it is. Omega transformation (converted to odds) This will give you a better outlook.

By the way, ratio data usually has the property of "the larger the better" or "the smaller the better". However, this does not mean that it is better to use the telescopic characteristics and the small characteristics, but the telescopic characteristics may be better. This story lies in Classification of Characteristics.

### Zero preferably target characteristics

In quality engineering, it is customary to explain the desired characteristics and dynamic characteristics from the signal-to-noise ratio, and to explain the zero desired characteristics as if they were their applications. The telebosis is an application of the telebosis microtrait.

The above is a data science for ease of understanding, and the zero expectation characteristic was made first.

The zero-hope characteristic basically uses variance as a measure of variation. It is the same as general statistics. As you can see on the page Assessing differences in variation for small data, it may be better to think of it as "considering the evaluation of differences in variability and defining including logarithms."

## Preferably target characteristics

In the above, the signal-to-noise ratio of the desired characteristic is almost the same as the reciprocal (1/coefficient of variation), whose formula is the coefficient of variation.

The formulas differ in the official definition formulas in textbooks, etc., and the SN ratio of the energy ratio type and the fluctuation ratio type. It correlates with the coefficient of variation pretty neatly, so what you're aiming for in the measurement is the same.

On this site, we write that the desired characteristic is "a characteristic in which the size of the average affects the variation." However, the desired characteristic is often explained as "a characteristic with a fixed target value".

Indeed, the literal meaning is "a characteristic for which the target value is determined", The calculation formula is the same as the coefficient of variation. "When the average increases, the variability also increases, and the effect of the increase in the average can be subtracted." I think it's harder to use it incorrectly.

## Actual calculations

In the actual calculation, the data is divided into groups, and for each of them, the signal-to-noise ratio is calculated and analyzed. The specific procedure can be found in Outside Arrangement of Orthogonal Array.

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