can i block runs in a DOE after the experiments are run?

[#1]

Hello,

i am wondering if it is possible to group runs into blocks after i have run all experiments in a DOE.  

i would do this in the case that i can't control how many runs i am able to do per day (maybe due to random equipment downtime or other uncontrollable factors), and i would like to group runs done in a single day into blocks.  typically, it seems like runs are grouped into blocks at the planning phase of the DOE, not after the DOE has been run, like i would like to do.

thanks!

[#2]

I would say yes, you could add a block to the design after it has been run, BUT the design would not be optimal for the blocking. If you know it will occur, you should account for it in the design phase to ensure optimality/balance. By adding it at the end you run the risk of confounding a factor with the block, having some blocks much larger than others which could increase the variance of your parameter estimates, which affects the testing of those parameters. You may also determine that not enough runs were completed to meet your analysis needs with the added block.

Based on the description you have provided, I would recommend going with block sizes that are small enough to ensure you can accomplish it in a day, even if things go wrong. If you find that you cannot get an entire block completed in a day, that skip the experimentation that day. That is the purpose of a DOE: plan what you are going to do. In my opinion, adding a block afterwards should only be a last-ditch effort to "rescue" a design that did not go according to plan.

[#3]

I wonder if you had hard to change factors in this experiment. Were one or more factors set once and kept at the same level for more than one run in a day?

[#4]

no, in my case i operate a shared tool that is connected to a mainframe which has several other tools connected to it.  even with easy to change factors, there is alot of unpredictability in the "up time" of the my tool based on other users on "my" tool and the events occurring on the other tools. These circumstances often makes it difficult to execute a pre-planned DOE.  i think Dan's suggestion above it good, which is to be conservative with the amount of runs i can do in a day.

[#5]

My thoughts:

Why can't you plan to use the tool and communicate to others using other tools to provide time for you to do this?  Is this simulation software you are running?  If so, blocking won't be very useful.

Blocking is a technique used to handle the factors you are unable to control in an experiment situation (i.e., noise).  The idea is to hold those factors constant (or sample such they don't vary) within the block thereby increasing the design precision and then purposely change those between the blocks to increase the inference space.  What noise changes within day and between day in your experiment situation?  Do you have hypotheses to support there are sources of variation acting between day and they have some effect on your response variables?

[#6]

i am mainly trying to figure out what to do if experiments don't go as planned and i am not able to execute the blocked DOE as planned.  we do schedule time, but it can still be chaotic due to the complexity of the tools and the number of people using the tools.  these are not simulation runs

[#7]

To reinforce the first sentence of @Dan_Obermiller's post: If you can run 100 experiments some days and 20 others I would have a hard time limiting every day to 20 runs.  Yes it would be nice to have each day neatly blocked together and optimized, but if extra runs on the days you can run 100 are inexpensive then why not run them?  If you just add the blocking variable later as you suggested sure you might find that you don't have enough runs at the end and you might not have used the smallest possible number of runs, but if you could have done twice as many runs in the same time then it might not matter.  Perhaps you could create the experiments with blocks of 20 and then throw that column out, execute the runs in order, and then add the day blocking variable.  That way if some days have 20 runs and some have 60 they would still be closer to optimal.

If some days you can run 20 experiments but every once in a while you only get 18 then sure you might just run 18 per day.

As to your question about what to do if things don't go as planned: If you find some new factor that might have affected your experiment, like the day, then sure you should add that to your model.  You just need to be careful about what conclusions you draw, if you add a new variable that you weren't controlling then you might not be able to infer cause and effect.