How do I analyze an unbalanced incomplete block design in JMP?

[#1]

I am considering a DOE situation where I want to block the runs by day to account for hidden variability between days.  At the same time, the test facility cannot reasonably measure the same number of runs each day.  They want to measure as many points as possible each day.  How do I maximize the use of the facility when things are running while also blocking the runs in a statistically valid manner?  What is the best method for designing and analyzing an experiment under these conditions? 

For the facility, lets assume if things go bad, the number of runs in a day might be only 3-7, and if things go well, the number of runs in a day could be anywhere from 15-25.  My thought was to set up the blocks with 15 runs/day, understanding that we will reach that some days but not others. 

I think this scenario is referred to as an unbalanced incomplete block design, or mixed model design, and the appropriate anlysis method would be Skillings-Mask Test, which is only available in JMP Pro.  Is this the most statistically correct method?  What are my options if I only have basic JMP?

[#2]

It’s nice to be able to plan your blocks and have them be orthogonal, but when you can’t, it’s not that big of a deal. The probability that your blocks become highly correlated with your fully randomized factors is pretty low. Just run it and keep track of when the runs are completed.

As for the analysis, I think you’re overthinking this. Just add your day block as a random effect and do everything else normally.