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Community Trekker

## 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.

9 REPLIES 9
Staff

## Re: Signal to Noise Ratio (S/N)

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

Learn it once, use it forever!
Community Trekker

## Re: Signal to Noise Ratio (S/N)

Hi mark,
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

Community Trekker

## Re: Signal to Noise Ratio (S/N)

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

1. Larger-The-Better (or LTB that maximizes the response) defined as:  S/N=-10*log(∑(1/Y2)/n)
2. Smaller-The-Better( or STB to minimize the response) defined as: S/N=-10*log(∑(Y2)/n)
3. 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
4. The JMP documentation for DOE and selecting the Taguchi Array button give you the steps for setting it up
Staff

## Re: Signal to Noise Ratio (S/N)

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.

Learn it once, use it forever!
Community Trekker

## Re: Signal to Noise Ratio (S/N)

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.

Community Trekker

## Re: Signal to Noise Ratio (S/N)

If NTB or STB is the objective for Y, simply apply the appropriate formulas in the newly created columns
Community Trekker

## Re: Signal to Noise Ratio (S/N)

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.

Staff

## Re: Signal to Noise Ratio (S/N)

I still do not understand what you mean by 'signal' and 'noise' of the model.Stating that the S/N is simply the signal to noise ratio isn't any more informative. What do you use for the signal and the noise for the model?

Also, how were thresholds of CV < 10 and S/N > 4 determined?

Thanks!

Learn it once, use it forever!
Community Trekker

## Re: Signal to Noise Ratio (S/N)

Taguchi’s optimization philosophy sought find the best levels of control factors that would maximize the Signal-to-Noise (S/N) ratios based on Orthogonal Arrays (OAs). OAs, were balanced with respect to all the control factors with the minimum number of experimental trials. This in turn implies that the resources (materials and time) required for the experiments are also minimum.

Taguchi method divided all problems into Static or Dynamic categories. Dynamic problems had SIGNAL factors. Static problems do not have any signal factors so optimization was achieved by using the three S/N ratios (S, LTB, NTB). Dynamic problems optimized using two S/N ratios that included Slope and Linearity.

Taguchi had over 80 different S/N ratios for use in different engineering situations, even though the most widely used S/Ns were STB, NTB, and LTB.

Taguchi Methods used an 8-step process of planning, conducting and evaluating results of matrix experiments (ranging from Plackett-Burman type designs to other fractional factorial forms) to determine the best levels of control factors. The main goal was to keep the variance in the output very low given the presence of noise inputs. These considerations led to more robust products and processes.

Doug Montgomery’ in his Discover Summit 2015 “Flight of the Phoenix” address pointed out that even though the approaches Taguchi used were controversial; he “got the problem right”.

As Mark said it is important to be clear on what is meant by the S/N ratio and it’s importance for the objectives of the study where it is used.