force levels in DoE

[#1]

Hello,

I was asked to build a DoE with continuous factors. However, the client wanted to have some levels (up to 5 for some factors) tested.

How may I force a custom D-optimal design to use these levels?

I thought bouilding the D-optimal DoE entering the factors as discrete numeric with the desired levels and then analysing them as continuous when the DoE has been performed.

Is there any better way to deal with this?

Thanks!

PY

[#2 · Accepted solution]

Hi @PYS,

I am wondering how adding a certain number of levels really help or support your objectives for this study and DoE ?

• Why does the client want additional levels ? Does he expect some curvature in the response, or other non-linear effects ? Does it correspond to levels frequently used ?

1. If you're in a screening phase with 5+ continuous factors (as this seems to be the case since you're mentioning D-optimality), you may be interested in Definitive Screening Designs, efficient designs that can detect interaction and quadratic effects. This design will create 3 equally distant levels (coded -1, 0 and 1) for each continuous factors.
2. You can also use Custom Design with continuous factors, and specify in the model higher order effects to "force" the design generation to introduce additional levels : for example, adding up to 2nd order term X4.X4 will create 3 levels for X4, up to 3rd order term X4.X4.X4 will create 4 levels in the design for X4, etc...

If you need to specify specific levels for this factor and these levels shouldn't be equidistant, then you can use Discrete Numeric factor and specify the appropriate terms in the model (JMP should do it by default with these terms specified as "If Possible).

Note that for the same runs number, increasing the number of levels for a factor decreases D-Efficiency, as the parameter estimates are less precisely estimated : instead of using runs only at -1 and +1 levels to estimate the slope of the effects for the response, you have more levels and less repetitions of these extreme levels, so the slope is less precisely estimated.

Hope this answer will help you,

[#3]

Hello Victor,

Thanks for the reply and the tips.

I agree that adding levels doesn't help and generally I only use the highest, lowest and if curvature estimation is required, the mean level. But in this case, I guess the client doesn't know much about DoE and so required specific levels to be tested. My main concern was regarding the choice of the best combinations while keeping the number of experiments sufficiently low. Indeed, we have 4 factors and only 1 must have the requested 5 levels.

When analysing the data, only main effect, two-factor interactions and quadratic effects will be investigated.

Unfortunately, we sometimes have to follow the desiderata of the funders

Have a nice day!

[#4]

I would ask the client if they are interested in understanding the causal structure to build a useable model or are they trying to pick a winner?

[#5]

Thank you for answering, you made my day.

[#6]

You can use the covariate factor type to force an optimal design to use specific factor levels. In the Custom Designer, covariate factors offer a general purpose solution for any time you have predetermined levels or a predetermined candidate set of runs. See this two-part blog post (pt. 1, pt. 2) for a description of covariate factors and their uses, as well as how to work with them in the Custom Designer. Here's the relevant section of the documentation.

Here is an example workflow in which the Customer Designer will produce an optimal design that includes each of five predetermined factor levels at least once:

1. Create a five-row data table with one column containing each of the five factor levels you want to force into the design.
2. Add a covariate factor in the Custom Designer. JMP will prompt you to select a column that contains the levels this factor can take. The design window will now display the values found in that column under Covariate/Candidate Runs; click to highlight all five.
3. Add your other three factors and continue through the design process.
4. When you get to the design generation at the end, you'll see check boxes to specify whether the design should include all levels highlighted in Step 2 (here, yes) and whether the design should be able to repeat covariate factor levels (here, yes).
5. Specify the total number of runs, and make the design.

If you need control over how many times each level appears in the design, the table in Step 1 should reflect your requirements. (E.g., if you want a 20-run design with four runs at each level, create a 20-row table with each level appearing four times.) Then in Step 4, do not check the box that allows repeated covariate runs.