5.
Process Improvement
5.3. Choosing an experimental design 5.3.3. How do you select an experimental design? 5.3.3.2. Randomized block designs


These designs handle 3 nuisance factors  GraecoLatin squares, as described on the previous page, are efficient designs to study the effect of one treatment factor in the presence of 3 nuisance factors. They are restricted, however, to the case in which all the factors have the same number of levels.  
Randomize as much as design allows 
Designs for 3, 4, and 5level factors are given on this page. These
designs show what the treatment combinations would be for each run.
When using any of these designs, be sure to randomize the
treatment units and trial order, as much as the design allows.
For example, one recommendation is that a GraecoLatin square design be randomly selected from those available, then randomize the run order. 

GraecoLatin Square Designs for 3, 4, and 5Level Factors  
Designs for 3level factors 
L_{1} = 3 levels of factor X_{1} (block) L_{2} = 3 levels of factor X_{2} (block) L_{3} = 3 levels of factor X_{3} (primary) L_{4} = 3 levels of factor X_{4} (primary) N = L1 * L2 = 9 runs


Designs for 4level factors 
L_{1} = 3 levels of factor X_{1} (block) L_{2} = 3 levels of factor X_{2} (block) L_{3} = 3 levels of factor X_{3} (primary) L_{4} = 3 levels of factor X_{4} (primary) N = L1 * L2 = 16 runs


Designs for 5level factors 
L_{1} = 3 levels of factor X_{1} (block) L_{2} = 3 levels of factor X_{2} (block) L_{3} = 3 levels of factor X_{3} (primary) L_{4} = 3 levels of factor X_{4} (primary) N = L1 * L2 = 25 runs


Further information  More designs are given in Box, Hunter, and Hunter (1978). 