In an augment design, how is the recommended number of runs for the newly added model terms determined, and how does this recommended number change relative to the original number of runs?

[#1]

In an augment design, how is the recommended number of runs for the newly added model terms determined, and how does this recommended number change relative to the original number of runs?

[#2 · Accepted solution]

Hi @CompositeCamel5,

You have several ways to augment a design, adding space filling runs, replicating, fold-over, adding centre points and/or axial runs, or adding runs to fit a specific model : Augmentation choices

In the last case, the recommended number of runs corresponds to the number of runs of the initial design + the number of runs required to estimate the effect terms added in the new model. It is hard to be more specific without any toy datable or without knowing from which design and model you start from, and which model terms you have added to get to your situation.

If you started with an RSM model for 4 factors with 16 runs (because of 15 terms to estimate: 1 intercept, 4 main effects, 6 interaction effects and 4 quadratic effects), then adding higher order terms up to 5th order for each of the 4 factors require the estimation of 12 new terms effects (3rd order, 4th order and 5th order polynomial effects for each of the 4 factors, so 12 polynomial terms) added in the model, hence the recommendation of JMP to add 12 runs to your initial 16 runs design, for a total of 28 runs.

Hope this answer will help you,

[#3]

Thank you very much for your response. Suppose the original model consists of only seven main effects with 16 experimental runs. Now, when using an augmented design to add second-order interaction effects to the original model, according to your previous explanation, the recommended number of runs after augmentation should be 37 (16 plus 21). However, in practice, the recommended number of runs after augmentation in JMP is 30. Could you please clarify if there are differences in the rules for determining the recommended number of runs between adding interaction effects and adding polynomial terms (powers)? Additionally, if block factors are included, will this introduce new impacts on the recommended number of runs after augmentation?

[#4]

I'm sorry, I made a mistake in my earlier observation. Now I fully understand. Thank you very much for your help!

[#5]

I would also like to ask another question: In an augmented design, if the original experiment includes block factors, when conducting an augmented design for the original experiment, it is found that the number of experimental runs recommended for the augmented design (after adding model terms) is not simply the sum of the number of runs in the original experiment and the number of newly added model terms. How should the number of recommended experimental runs be calculated when performing an augmented design that includes block factors?

[#6]

See my answer here: https://community.jmp.com/t5/Discussions/In-an-augmented-design-if-the-original-experiment-includes-...

It depends on the number of newly added terms, as well as the number of runs per block that you have specified, as JMP will try to recommend an augmentation scenario with similar block size respecting your constraint of k runs per block.

Hope this answer will help you,