Blocking and Factorial Design

When blocking has to be implemented due to either a very large number of runs that need to be run over multiple days or equipment limitations that could make each individual run not be identical, it is necessary to develop an appropriate structure to minimise these effects on the overall design. 

The easiest approach is to treat the blocking variable (day or run) as an additional factor in the experiment and then design a fractional factorial 

Consider the case where we have a full 2 factorial experiment that must be run in 2 blocks of 8 runs (two days). Assume that it is known that the AB interaction is zero. Design an appropriate experiment that maximises the informatiOTi that can be extracted. 

In general, whenever one is faced with a blocking issue with known variables, then the problem can be reduced and analysed as if it were a fractional factorial design with additional dummy variables. In this particular example, let the original factors be A, B, C, and D and let the blocking variable be an additional fifth factor, E. Since we have been told that the AB interaction is zero, in order to minimise the confounding, let E = AB. All runs 

All experiments with (+) in the final column and in light grey would be run on 1 day and those with a (-) in the final column and in dark grey would be run on another day 

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