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Signal to Noise Ratio (S/N)

Hi guys,

Glad to be part of this great community. Looking forward to making useful contributions.

I need some help with determining the Signal to Noise Ratio (S/N) for my regression model. I am using JMP pro 11 software.

Can anybody help me please? Thanks.

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Mark_Bailey

Your question lacks a lot of detail but it sounds like a question about setting up a Taguchi response.

Hi mark,
Many thanks for your response.
So basically, I am carrying out a DoE based study of a chemical reaction (Fenton oxidation). Four independent variables and one dependent variable were fit into a Central Composite Design to generate a polynomial function and model. To assess the accuracy of the model predictions, I need to look at some statistical parameters i.e. the coefficient of determination (R2), ANOVA, LOF, Coefficient of variation (CV), Adequate precision (also known as the Signal to Noise ratio S/N)). I do not know how to find the S/N of the model. And No, I haven’t used a Taguchi design.

Thanks

melvin_alexande

Taguchi S/N ratios come in 3 basic forms, depending on what your objective for the response variable (Y) is

Larger-The-Better (or LTB that maximizes the response) defined as: S/N=-10*log(∑(1/Y2)/n)
Smaller-The-Better( or STB to minimize the response) defined as: S/N=-10*log(∑(Y2)/n)
Target-The-Best (or TTB to target the response, basing the S/N ratio on a-means and standard deviations or on b-standard deviations only) defined as: (a) S/N=-10*log(∑(Yhat-s2/n)/s2) or (b) S/N=-10*log(∑(Yhat)2/s2), what JMP uses
The JMP documentation for DOE and selecting the Taguchi Array button give you the steps for setting it up

Mark_Bailey

So I am sure that you found the other metrics that you mentioned. JMP does not report a S/N for the model. Can you tell me how the S/N is defined that you need?

The answer might be to save formulas for the model and other statistics, and then compute it in a new column.

melvin_alexande

The Byrne-Taguchi Example in the Sample Data file installed with JMP has LTB formula columns for the Mean Y and SN Ratio Y when clicking the Make Table command.

You can copy and paste these formulas into new formula columns for the factor setting combinations in the CCD once the data are collected.

JMP pro 11 provides the other metrics by default with the exception of the coefficient of variation, which I simply computed as the ratio of RMSE to the mean of the response multiplied by 100.

The vast majority of publications, which use the DoE methodology in my subject area, look at all of the metrics (I mentioned the previous response) in validating a model. The common view is that a good model should have a CV < 10 and an adequate precision (S/N) > 4.

Most papers define the S/N simply as the signal to noise ratio. Admittedly most studies, which reported this parameter used a different software, e.g. Design expert and Matlab.