DOE Augment design - Suggested runs change every time and have non-Integer numbers

[#1]

Hello,

I have done a half-factorial screening with 4 factors, and now would like to augment the design to include the rest of the missing 2-way interactions and axial points to check for quadratics. 

When I use the DOE -> Augment Design ->Augment-> RSM and 2nd interactions, the number of suggested runs is always 18 (10 previous runs and 8 new runs as the augmented design) , however, the actual runs change every time that I try these same steps. I have two examples pasted below.  I'd like to know why does this happens and why the runs change.

And my second question is regarding the "weird" non-Integer values suggested by JMP (56.6 and 57.2 in the tables below - the range for that factor has been set to 50-70). Why does JMP require a run at these specific values instead of the mid point which in this case will be 60? Is this related to the optimality criteria (D-optimal vs I-optimal)?

Thank you in advance!

[#2 · Accepted solution]

I am not sure why the number of suggested runs changes each time. It might depend on the specific steps you took.

A fractional factorial design uses combinations of given levels. Augmentation uses custom design, which creates the levels with the algorithm. The optimality is sometimes improved with off-center levels, but you can set them back to the integer value with little loss in optimality.

[#3]

Thank you for the response!

The number of suggested runs does not change ( it is always , but the values of the factors in those 8 runs change. For instance, in the first try, JMP suggested to run with factors at levels (4,2,15,56.6). But this combination does not appear in the next try.

[#4]

There are multiple options of extra runs which will give the same/similar optimality.

[#5 · Accepted solution]

The augment design feature does not really put much thought into the number of runs that are suggested. It will always be 8 unless you specify a larger model that will require more than 8 additional runs. 

For example, create a design for two factors, main effects only model. Now choose augment and you will see the number of additional runs is 8 more than your design. Try another example with 20 factors. Again, stick with main effects only model. Augment will again add 8 more runs. 

Bottom line is that do not put any consideration into the 8 additional runs. You need to specify the appropriate number that you can do that will allow you to meet your power and prediction precision.

For your four factors, there are 6 two-way interactions. There are four quadratic terms. Your augmented design will be fitting 10 additional model terms from where you started (which was 5 terms - intercept + four main effects).  I would recommend starting with at least 10 additional runs in your augmentation, possibly more to meet the appropriate prediction precision.

[#6]

The combinatorial design methods are deterministic. They will always arrive at the same result. Augmentation in JMP uses Custom Design. Custom Design, though, is an algorithmic method that starts with a (horrible) random design for the new runs. It iteratively improves the design until the chosen optimality criterion is optimized. Hence, we call it optimal design. The random starting point is one reason you are not guaranteed to arrive at the same result. In fact, Custom Design does not search once for the optimal design. It might be locally optimal, so it repeats the search process many times. Each time it starts with a new random design.

Also, it is often the case that there is more than one design with the same optimality. JMP can no longer distinguish designs. Repeating the augmentation process is likely to arrive at a different result.