topic Analysis of Plackett-Burman design in Discussions

Analysis of Plackett-Burman design

SaraA — Wed, 10 Apr 2024 13:27:38 GMT

Hi all,

I have run a Plackett-Burman foldover screening DOE using 9 continuous factors. I included 3 center points to detect curvature.

I am unsure if for the analysis of the data table I should run the 'Screening' script or use the fit model platform. If I use the fit model platform, should I only include the main effects to construct the model effects since a PB design only allows estimation of main effects? When doing this, I have a significant lack of fit test and the model it does not detect curvature. Whilst when I use the screening script the lack of fit test is non-significant and I see that for some factors, the relationship with the reponse is non-linear.

Thank you for your help.

Sara

Re: Analysis of Plackett-Burman design

SaraA — Wed, 10 Apr 2024 13:59:14 GMT

I also do not understand why this Screening script appears for this PB design while it was not present for a main effects screening design that I performed a few months ago.

Re: Analysis of Plackett-Burman design

Mark_Bailey — Wed, 10 Apr 2024 18:20:19 GMT

The P-B designs can potentially estimate more than the main effects. They might produce correlated estimates for some terms, but they generally avoid confounding by using regular fractional factorial designs.

The Screening platform is a bridge to the Fit Least Squares platform. Its sole purpose is term selection before estimation.

The lack of fit is presumably because the replicated runs (center points) exhibit less variance than the model. Select the center points. Please give them a unique color (not black) and exclude (not hide) them. Run the model in Fit Least Squares again. You won't have a Lack of Fit test, but you can see the center points in the Actual by Predicted plot at the top. Are they out of line with the rest of the runs?

Re: Analysis of Plackett-Burman design

roberrtt — Thu, 11 Apr 2024 06:53:57 GMT

Thanks for these insights mate

Re: Analysis of Plackett-Burman design

SaraA — Thu, 11 Apr 2024 15:05:57 GMT

But how exactly does the Screening platform select the terms/two-factor interactions?

After excluding the centre points I still get a lack of fit test because I have three replicates for all my runs.

Using the Screening platform gives me a non-significant lack of fit test. Can I proceed with using the Screening Platform instead of the Fit Model platform as I am unable to know which terms to select in the Fit Model based on current knowledge?

Re: Analysis of Plackett-Burman design

SaraA — Thu, 11 Apr 2024 15:16:55 GMT

This is what I found in the DOE guide:

• If your factors are all two-level and orthogonal, all of the statistics in the Fit Two Level Screening platform are appropriate.

When can I assume that my factors are orthogonal?

• If you have data from a highly supersaturated main effect design, the Fit Two Level Screening platform is effective in

selecting active factors, but it is not effective at estimating the error or the significance. The Monte Carlo simulation to produce p-values uses assumptions that are not valid for this case.

I do not think this is a problem for a PB design.

• If you have a categorical or a discrete numeric factor with more than two levels, the Fit Two Level Screening platform is not appropriate.JMP treats the associated model terms as continuous. For such factor, the variation is scattered across main effects and polynomial effects. In this situation, it is recommended that you use the Fit Model platform.

I only have continuous factors.

So based on these assumptions, can I proceed then proceed with the Screening platform?

Re: Analysis of Plackett-Burman design

Mark_Bailey — Thu, 11 Apr 2024 15:21:26 GMT

Please read the chapter about the Fit Two-Level Screening platform.

This platform is intended for continuous factors. It creates an orthogonal contrast for each term. It begins with the main effects and then adds a contrast for higher-order terms until the model is saturated (zero degrees of freedom for the error). This approach is based on the key screening principles of effect sparsity, effect hierarchy, and model heredity. Individual and simultaneous p-values are computed for each contrast. A normal plot of the contrasts is provided.

Re: Analysis of Plackett-Burman design

Mark_Bailey — Thu, 11 Apr 2024 15:24:24 GMT

It is likely that the response has non-linear effects that are not accounted for by the main effects alone.

Do the terms selected by the Screening platform make sense? Does the model include higher-order terms that might account for the lack of fit?

Ambiguity about the model is an acceptable part of screening. Screening is usually followed by augmenting the original design with new runs to an augmented model to account for lack-of-fit or test additional effects.

Re: Analysis of Plackett-Burman design

Mark_Bailey — Thu, 11 Apr 2024 15:28:45 GMT

The design that you choose determines if the factors are orthogonal. The factors in a P-B design are orthogonal.

A P-B design is not super-saturated.

The Screening platform is appropriate for two-level P-B designs. Remember that each method of analysis or term selection has its own assumptions and approaches. You should not expect exact agreement across platforms or options.