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Level III

## Sample Size for DOE

Hello,

I write you to have some suggestion regarding on topic linked to the DOE.

I have a industrial process. The outout (response) of the process is the percentage of scrap.

The average of this scrap is around 1.5%.

I want to create a DOE to identify main factors, interactions, model,...

My question is: how I can determine the number of the replicates for each corner (for a specific power) to be sure to have correct statisical results (if in one trial I will obtain "0% of scrap" it is real output change or only a case)?

Best Regards,

Simone

11 REPLIES 11
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Super User

## Re: Sample Size for DOE

Are you using Custom Design or something else?  Look at the design diagnostics in the DOE platform that appears after generating your design.  There is a power analysis at the top of that report.  Basically, you check the power and keep adjusting the number of runs until you're satisfied.  If you're using Full Factorial, consider using Custom Design instead as placing additional points on the corners is not always the best allocation of additional runs, particularly if you have any quadratic terms.  If you do have quadratic terms, run sizes that are divisible by both 3 and 2 tend to work well.

-- Cameron Willden
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Staff

## Re: Sample Size for DOE

Adding to @cwillden , you have several ways of specifying your power requirements to determine the minimum sample size. You can specify the response SD (RMSE) and the anticipated coefficient as half the minimum effect size. For example, if you want to find a real effect of a change of 0.5%, then enter 0.25% for the coefficient. Alternatively, you can set the RMSE to 1 and enter the anticipated coefficient as have the multiple of SD you expect the response to change. For example, if you expect a real change of 3 SD, then enter 1.5 for the coefficient. The last way is to enter the RMSE and then the expected responses. Sometimes it is easier to think about the real changes this way.

i also agree with him that optimal replication will result from using Custom Design, rather than replicating another design.

Learn it once, use it forever!
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Level III

## Re: Sample Size for DOE

Thanks Marks... now is becaming more clear.

Best Regards,

Simone

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Level III

Best Regards,

Simone

Highlighted
Staff

## Re: Sample Size for DOE

The full factorial design method is the oldest. It provides excellent data for fitting the explanatory model! However, the method is based on combinatorics and is inflexible, which is the issue that you encountered. I think that the flexibility of the custom design method will be an advantage in your case.

Learn it once, use it forever!
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Level VII

## Re: Sample Size for DOE

Simone, I will offer a different perspective.

In my humble opinion, your question is the wrong one.  It is more likely: how many experimental units (or measures of the EU's) must be made to have a study (experiment) that represents (now and in the future) or exposes the phenomena of interest? The response variable of % scrap is a poor response variable.  There are too many failure mechanisms that are confounded in such a response.  It does not offer enough discrimination to be very effective for running experiments (particularly at the level % you are discussing).  So why are the "units" being scrapped?  Is it due to some diimensional, physical or cosmetic attribute?  For example; If "out-of-spec", use the actual measurements. If cosmetic, use an ordinal scale.  You may need to "create" a meausrement (or more than 1) to adequatly describe the phenomena.  Some other questions:  Is the scrap consistently being produced (or does it vary over time)?  Do you have any idea what measurement system error is? Is the process sequential?  If so, do you have hypotheses about where in the process the "scrap" is being generated? How much of the scrap is due to factors you can contriol and how much may be due to noise (factors you do not control).  If noise is the issue, you will need to have strategies to handle the noise in the experiment situation (e.g., RCBD, BIB, split-plots, repeats, etc.).  You will need to design experiments to create a process robust to the noise.

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Level III

## Re: Sample Size for DOE

Thank you for the details (some of them generated in me some more interesting question).

One details: in this moment (for this process) the output is only "pass" / "fail" coming from a visual inspection (linked a type of color).

Best Regards,

Simone

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Staff

## Re: Sample Size for DOE

I forgot about your binary response. You might consider designing the experiment for the linear model but analyzing the data with logistic regression (non-linear response with a linear predictor).

Do you have JMP Pro? If so, you can use the built-in simulator to assess power for such a case. I can lead you through the process.

Learn it once, use it forever!
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Level III

## Re: Sample Size for DOE

Hello Mark,

in this moment I have not JMP Pro... but I take note of your input.

Thanks.

Simone

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