# Constrained design of experiments

I would like to conduct a 2-level fractional factorial experimental design on 8 factors. I used the FrF2 package in R to do so. I have capacity to do roughly 30 experiments, so I selected a resolution IV 2^(8-3) with one center-point. Repeats aren't necessary for reasons related to the quasi-computational nature of the experiment. Upon inputting the values to the machine controlling the experiment I realized the following. Two of the factors, call them A and B, would normally have (A,B) permutations equal to (False,False), (False,True), (True,False), (True,True). However, the (True,False) combination does not make physical sense - it is impossible. But the other three combinations do make sense and I would like to test them. I am unable to find information on how to properly account for this case to design an efficient experiment with few aliases. Any help with this would be greatly appreciated.

• If repeats aren't necessary, then what do you intend to test? Aug 8, 2018 at 4:49
• Hi Franz, the experiment is to measure the effects of various parameters on the duration of a computer-controlled manufacturing process. For a given set of parameters the variability is very low. There are many important and undetermined interactions between the parameters that I need to determine through measurement. Aug 9, 2018 at 8:58
• The variability, however low, is the only way you can report on the significance of any of the effects. Moreover, you will need sufficient degrees of freedom for your model to estimate interactions between variables. The only way to increase the degrees of freedom is by increasing the number of independent samples. Aug 9, 2018 at 9:02