discrete numeric factor good choice?

[#1]

I have 4 factors with 3 settings:- 

time- 5, 10, 20

water- 100, 200, 300

speed1- 2500, 3000, 4000

speed2- 5000, 6000, 7000

 my response is viscosity and trying to figure out at what setting can I get my desired viscosity. I am trying to set up a design. Since I have 3 settings of each factor I was thinking of using discrete numeric factor but I read in JMP documentation that "Not all levels of a discrete numeric factor appear in the design. The levels that appear are determined by your specifications in the Model outline". 

Is there anything specific I need to do to get all the levels? Is there any other type of factor other than discrete numeric factor to answer this question?

[#2 · Accepted solution]

The custom design algorithm must have consistency between the number of levels and the terms that appear in the model. For example, if you add a discrete numeric factor with four levels then custom design will add F, F^2, and F^3 to the model. The last two terms, though, should automatically have their estimability changed to 'if possible.' You can change the estimability to 'necessary' if you want to be sure to estimate these parameters, though.

The other influence on the appearance of the levels and treatments is the number of runs. You won't see many treatments if your choice is close to the minimum number of runs, which is determined by the terms that must be estimated.

Are these levels determined by humans or by equipment? For example, are those speeds the levels that experts think will work or are they the only possible settings on the equipment? It sounds like (but I could be wrong) that you want to 'pick the winner' from the observed combinations rather than interpolate with the model to optimize the viscosity. In that case, you could also use categorical factors instead.

I bet you have some interesting interactions with these factors.

[#3]

@Mark_Bailey thank you for your reply.

For number of runs I used the maximum number that was suggested by JMP.

These levels were decided by experts and they chose these levels to look at both passing and failing results. When you said I can use categorical factors you mean for all of them instead of discrete numeric using categorical? I did try using categorical before, but with that I will not be able to look at interactions.

Yes I looked at interactions as well and with maximum number of runs I can see lots of correlation between the factors in the correlation map. Attached is my design using dicrete numeric factors and looking at 2nd order interactions as well wih maximum number of runs suggested by JMP.

[#4]

Just to clarify, JMP does not suggest a maximum number of runs. JMP provides a default number of runs based on some simple heuristics. Feel free to choose another number based on the evaluation information, such as the power analysis.

Let me re-state your answer about experts choosing the levels to produce passing and failing viscosity. The change in the viscosity over the factor range will be 3-4 times larger than the standard deviation of the viscosity. Is that true?

Yes, I meant using the categorical factor type instead of the discrete numeric factor type for all the factors. You can estimate the interactions but the number of runs is much larger and likely not practical for you.

The correlations are unavoidable due to the specifications for this design. On the other hand, the worst correlation is about 1/3, so you still have the ability to estimate these parameters and if the effect is much larger than the standard deviation, with reasonably high power.

This design seems like a good choice, based on the information provided here so far.

Just a reminder: glad you came to the JMP Community for help! We will do our best. But I want to set realistic expectations. This area is not meant to provide consulting or training. It is meant to help with specific problems or issues. We can point to other resources if you need more extensive help with the design of experiments.

[#5]

@Mark_Bailey yes default number of runs not the maximum. Sorry about that.

Yes I understand the number of runs will be high with categorical.

Thank you for the discussion, my main question was to check if there is any other type or way for this design that I am not aware of. Thank you