JMP Custom DOE vs Full Factorial DOE

SajithD

Hi,

 

I'm new to JMP. I would like to learn and understand the difference between the Custom DOE design and the Full Factorial DOE design. I am designing an experiment using 4 variables (2 levels each, 4th variable is categorical). A full factorial requires 16 runs. When I build the experiment in Custom design however, the default # of runs in JMP is 12. Why are the # of runs in each of these different? I get why it is 16 in the full factorial (2^4). But why is JMP recommending just 12 in the custom design? What's been assumed/factored into each of these designs?

 

I would greatly appreciate any help on this!

 

Thanks,

Sajith

 

 

cwillden

That's a whole course of study contained in that question, but I'll try to summarize as best I can.  Custom Design is built on a completely different paradigm of "optimal" or "algorithmic" designs.  Full factorial designs are a classical type of DOE.  They enforce all possible combinations of factor levels into the design.  This gives the design some very desirable properties, such as orthogonal effects (no correlation between model terms, so coefficients are estimated with maximal precision for given number of runs).  You can also estimate all main effects and higher order terms up to n-way interactions for n factors.  However, you'll find that these designs quickly explode in size.  A full factorial with 8 factors, each with 2 levels, has 2^8 = 256 runs.  In most cases that is way too many runs.

 

In classical designs, you would look to fractional factorials to reduce the number of runs.  These designs strategically confound the higher order model terms in order to reduce the design size significantly.  In many cases, experimenters are only interested in main effects and 2 factor interactions.  So losing the ability to estimate an 8, 7, 6, 5, 4-way interactions is of little consequence.  For example, I could do a fractional factorial with 8 factors in only 64 runs (quite a bit lower than 254!), and still have uncorrelated main effects and 2-factor interactions, and can maybe even estimate higher orders than that depending on the level of fractionization.  These designs, amongst many other classical designs, are all derived from theory.

 

Optimal designs are generated from computer algorithms where you basically describe what you want as inputs into the algorithm, and it returns a design with the most optimal set of design points to meet your experimental objectives.  It does so through a process of rearranging design points (aka your run conditions) inside the design space until some optimization criteria is optimized (maximized for some criteria or minimized for others).  There are 2 really prominent optimality criteria, D- and I-optimality.  D-optimality emphasizes precise estimates of model coefficients (makes it a pretty good all-around choice, but excels in screening situations where people would commonly choose fractional factorial designs).  I-optimality emphasizes low prediction variance, and is more associated with response surface designs.  The basic idea is that while classical designs are very rigid and uncompromising, optimal designs can tailor an experiment to your needs.  I can do a decent design for the 8-factor situation with something like 48 runs and still be able to estimate all the model terms I care about (main effects and 2-factor interactions).  I pay for this convenience by allowing some partial correlations between the model terms, but that is often of little consequence.

 

You will find other optimality criteria in Custom Design.  A-optimality is a newer addition, and I think they are very compelling designs.