In quality engineering, S/N ratio is important index for functional evaluation. 

    Traditional S/N ratio   η=10log((Sβ-Ve)/VN)

 

Issues of traditional S/N ratio：

*It is impossible to compare with different repetition number.

*If you increase repetition size, S/N ratio also increased. It means S/N ratio value is changed by repetition number or signal size.

*(Sβ-Ve) shows negative number sometimes. And impossible to calculate logarithmic S/N.

These issues come from DF (Degree of Freedom).

 

KQERG proposed new S/N ratio for solving issue of traditional S/N ratio formula.

New S/N ratio formula is very simple to understand.

After decomposition of sum of square, you define active element and harmful element by customer requirement.

                  SS_total=SS_active+SS_harmful

                  Active/Harmful=SS_active / SS_harmful

Then  

                 S/N ratio  ηE =10log(SS_active/SS_harmful) (db)

 

Dyanamic character S/N ratio

                SS_total=Sβ+SNxβ+Se

                SS_active: Sβ

                SS_harmful: SNxβ, Se

New         ηE=10log(Sβ/(St-Sβ))

Traditional     η=10log((Sβ-Ve)/VN)

 

Static character S/N ratio

       SS_total=Sm+SNxβ+Se

       SS_active: Sm

       SS_harmful: SNxm, Se

 

nominal-is-best response

New            ηE=10log(Sm/(St-Sm))

Traditional        η=10log((Sm-Ve)/Ve)

 

New

smaller-is-better response       ηE=10log(n/St)   

larger-is-better response         ηE=10log(St/n)

zero-is-best response             ηE=10log(n/(St-Sm))

 

In US, Traditional S/N ratio   η=10log(m^2/σ^2)

m: Mean σ:Standard deviation (Se/n)