Why does the Default DoE Custom Design have so little sampling of middle levels?

[#1]

When doing a Custom Design, sometimes middle levels (other than the highest and lowest) are specified, so it is more than 2 levels. However, Custom Design Default design tends to suppress sampling of these middle levels, putting most weight on the highest and lowest of each parameter. How is this determined? Can we specify to add more in the middle?

[#2]

There are several various themes wrt to a response to your questions Hopefully others will add and comment?

To get you started...here goes: The JMP Custom Design platform uses a mathematical algorithm known as coordinate exchange to maximize what is known as a design optimality criteria. There are several optimality criteria available in JMP. The algorithm uses inputs such as the number of factors, the effects you would like to estimate in a model, and the number of runs to determine a default optimality criteria, the specific design, and the levels within the design as well as additional considerations such as disallowed combinations, hard to change or very hard to change factors, replication, and others. The user has the ability to 'force' JMP to use a different optimality criteria if you so choose. Not a path I'd recommend...but it can be done. And finally yes, you can add runs to a design that JMP creates. A good place to start there is the Augment Design workflow. A warning if you willy nilly add treatment combinations to an existing design, you may reduce the optimality criteria, and also change other design criteria that might reduce the efficiency or power of your design for it's intended practical purpose. Again...not recommended. Use the JMP Augment Design platform to avoid these issues.

Here's a link to the JMP documentation explaining the various optimality criteria supported: Optimality Criteria 

Here's a link to more details wrt to the coordinate exchange algorithm: Coordinate Exchange Algorithm 

Here's a link to the Augment Design platform/workflow: Augment Design 

[#3]

@P_Bartell has much more knowledge of the custom design platform in JMP, so I defer to his advice.

On a practical note, the resolution of the design (linear) and the degree the design lets you approximate (polynomial) are both considerations in design selection.  Remember, this is an experiment to understand the causal relationships, not a test to "pick the winner". I am an ardent believer in the sequential (iterative) nature of investigation (scientific method and model building).  Therefore, I often begin my investigations by understanding 1st order linear terms (which allows for testing categorical as well as continuous variables) and augment those through iteration (adding resolution and the ability to estimate non-linear terms which might start with center points).  

I also believe there is way too much emphasis on the design structure and not enough is spent on understanding the noise structure (through blocking, repeats, nesting, split-plots, et. al.).  That being said, the design you choose should be one that answers the questions you pose or provides insight to your hypotheses.

For your situation, it seems you are interested in the quadratic relationships.  Why?  Do you already have a first order model?  Are you concerned your level setting will "miss" an important effect between those levels? Are all of your factors continuous?  Are you familiar with the guiding principles of Scarcity, Hierarchy and Heredity?