Centre point vs factor level

[#1]

Hello:

I am studying a DOE textbook and in one example there are two factors with two levels.

A 2^2 experiment is set-up with 5 center points. There are no replicates or blocks. In total 9 runs

My question is what is the benefit of CP, why not a two factor experiment with three levels, In total 8 runs

Q1) Which scenario is more beneficial?

Q2) Are there any cases where we should use CP and where we should use an additional level?

Your help is highly appreciated.

Best Regards,

Varun Katiyar

[#2]

Hi @VarunK,

Did you check my previous answer to one of your previous post about the differences between middle points and centre points ?

https://community.jmp.com/t5/Discussions/effect-of-centre-points/m-p/671637/highlight/true#M85961

In my answer, I tried to explain that there are different uses between "middle" points (to test and estimate specific quadratic coefficient terms) and centre points (test for curvature, lack-of-fit test, decrease variance prediction in the centre of the experimental space, ...), so I think your two questions were already answered in the previous post.

There is no scenario "more beneficial" than another, just some scenario that is perhaps more adapted to a specific objective than another. Please read again my answer on your previous post, and check it as solution if you have found the answers you're looking for, that will also help other members to spot directly the info they are looking for.

[#3]

Hi Victor:

Thank you very much for your time.

I did read your previous answer and based on that had some more questions which I tried researching but could not find answer.

If I take the textbook example, a 2^2 full factorial design with 5 CP and my subject of interest design of 3^2 (both the factors have three levels instead of 2) design, both the scenarios have 9 experimental runs, what are the benefits of each run.

1) CP runs will help in curvature detection (but not tell which factor if curvature present) and help with Pure error and hence increasing power

2) Three level runs will help with curvature detection and also identifying the factor and I believe will also increase the power (by smaller value compared to CP runs) but will not give Pure error.

So, I was trying to understand what will cause the researcher to choose any option.

Your help is highly appreciated.

[#4]

Below is the power comparison of both the designs.

Power of intercept is lower in 3^2 design compared to 2^2 design with cp, rest all are greater or almost similar.

I would have chosen 3^2 for this case but any more factors and 3^k design will be more expensive and time consuming and hence Response surface designs  or 2^k design with CP leading to central composite designs will be more beneficial.

Please let me know if there are any other details that I am missing  in comparison.

[#5 · Accepted solution]

As I was mentioning in the other post, there may be several points to take into consideration in order to choose/decide between the two designs possibilities :

• Study phase : Is this design part of a
  • Screening phase, so quadratic terms may be not necessary to estimate, but lack-of-fit test may be interesting to consider if the experimental area chosen is relevant to check if the model is adequate for the system under study,
  • Optimization phase, so you may need quadratic terms estimation to fit a response surface model, or
  • Robustness phase ; if you want to evaluate robustness of your optimal settings, the central point will correspond to the optimal conditions found before, and you want to be sure that the variation around this optimum is negligible, so middle points may not be needed here, and the emphasis is more on evaluating and reducing prediction variance in the centre of the experimental space than estimating complex terms in a model, since you expect no or little variation, so no statistically significant effects.
  • ?

• Domain expertise : Is there already prior knowledge about the need to estimate quadratic effects ? Does it make sense to consider quadratic terms for this system under study ? Or a more simple model may be enough to consider ?

• Goal (related to study phase): Are you putting emphasis on effects screening/statistical significance, and/or on predictive performances ? Depending on the goal(s), a design may be more appropriate than another. 

Also take into consideration that this example is a simple one with only 2 factors (so more an educational example), but if working with more factors, the gap in the experimental runs number between a design without quadratic effects estimation and and with these effects estimation can quickly become important.

These points are not exhaustive, but serve as illustration to explain you that design evaluation may be important to choose one design over another one, but the choice should also always take into consideration domain expertise, goal, and study phase to find the most informative compromise for the lowest number of experimental runs.

Hope this answer will help you,

[#6]

Thank you Victor for your time and knowledge sharing.