which factor type shold be choosen for custom design

[#1]

I am optimizing a production process and first want to evaluate the contribution of each factors to the response using custom design.

Factors include facility conditions, which are continuous variables, but in reality are very difficult to vary in value.(Length of jig, etc.)

For such variable, which factor type should I choose?
The facility conditions may have a significant contribution and I would like to find the optimal value, but the range of possible values, which I can vary is limited, I am unable to create a balanced experimental design.
On the other hand, if I treat it as a categorical or block variable, I am warring that I will not be able to infer the optimal value if this variable has a significant contribution.

[#2 · Accepted solution]

Hi @yukko,

Welcome in the Community !

If your factors are variable that can be measured, I would recommend using numerical factors. According to JMP Help about the description and difference between continuous and discrete numeric factors (Factors):

"A continuous factor is a factor that you can conceptually set to any value between the lower and upper limits you supply, given the limitations of your process and measurement system."

"A discrete numeric factor can assume only a discrete number of values. These values have an implied order."

So depending on the possibility to have intermediate values in the range of your numerical factors, you may opt to choose for numeric continuous (no constraints on factors levels choice) or numeric discrete (possibility to choose only certain levels for each factor) factors.

If you first want to evaluate the contribution of each factors to the response with a Custom design, the choice of the factors type may not be very impactful : as you're in a screening phase, you may choose 2 (min and max) to 3 (min, middle, max) levels for each factor, so the design and analysis will be quite similar with these two factors types.

With discrete numeric factors and 3 levels, you may choose an intermediate level that is not the middle level, unlike with continuous factors, and the model will automatically contain quadratic effects. The analysis will be a little different compared to continuous factors, as discrete factors are like ordinal factors (categorical but ordered).

With continuous factors, you can add in the model quadratic effects (and/or centre points) to add a third level in the design for those factors.

Hope this answer will help you,

[#3]

Thank you so much @Victor_G .

I understood that it should be treated as a discrete number.
On the other hand, if the type of variable is not very important in the initial screening phase, what is the difference between treating a variable as a continuous variable and a discrete variable?

[#4]

Hi @yukko,

The type of variable will not create differences in the design if you have 2 levels.
If you want 3 levels, choosing discrete numeric factors help setting the intermediate level at any chosen value in the factor's range, whereas continuous numeric factors require setting quadratic terms in the model (and/or centre points) to include a third level in the design (that will be automatically a middle point in the range of the factor). 

The big difference of treating numeric factor as discrete or continuous is about the interpolation, that means the possibility to predict the response(s) continuously at any given value between the levels used for continuous factor, depending on the regression model and terms used in this model. 

Profiler with X1 as discrete numeric and 2 levels (modeling done with the 2 levels but predictions can only be done by specifying one of the two levels studied): 

Profiler with X1 as continuous numeric with 2 levels (modeling done with the 2 levels but predictions can be done on the whole range of X1, from -1 to 1):

Hope this helps you understand the difference,

[#5]

hello @Victor_G .
Sorry for the delay.
I understand the difference between these two types of variables.
I understand that this difference has great significance in the next stage of screening, the optimization stage.
Thank you very much for your kind advice.