Reducing experiment numbers
DoE is a very powerful tool to efficiently look at the cause and effect relationship between factors such as temperature and concentration, and responses such as conversion and impurity formation. DoE looks at each factor at 2 or more levels.
At a recent conference we saw some misconceptions about DoE which may add to the confusion and reluctance around the use of experimental design and would like to clarify some points. The relationship between n factors and the number of experiments is 2^{n} for a full factorial design. Therefore, investigating 4 factors equates to 16 experiments, while 12 factors requires 4096 experiments if all experimental combinations are carried out. It is important to also include a centre point which is repeated to help check for nonlinear responses and to determine the experimental error for the design. Typically, three repeated experiments are carried out to determine the experimental error.
Full factorial designs investigating 34 factors are commonly carried out in industry, yet there are many different experimental designs that serve different purposes and you do not need to run a full factorial design where experiment numbers can still be high.
Fractional factorial designs look at the relationship between factors and responses, but higher resolution designs can also investigate and interpret interactions between factors (see below). In fact you can investigate the effects of 4 to 7 factors in as few as 8 (+3) experiments while up to 16 factors can be investigated in 32 (+3) experiments. The additional 3 experiments are identical centre points.
No. of factors 
Resolution III 
Resolution IV 
Resolution V 
Response surface 
Full factorial 
4 

8 
16 
24 
16 
6 
8 
12 
32 
44 
64 
12 
16 
32 
256 
280 
4096 
16 

32 
256 
288 
65536 
A resolution III fractional factorial design investigates the effect of changing each factor on the responses but is unable to explain any interactions.
A resolution IV fractional factorial design investigates the effect of changing each factor on a response and identifies if interactions are present, but will not be able to fully identify each interaction as there is some confounding.
A resolution V fractional factorial design investigates the effect of changing each factor on the responses and explains any 2way interactions.
Response surface designs investigate the effect of changing each factor on the responses, identifies interactions and investigates any quadratic terms to explain nonlinear effects by investigating each factor at 3 or more levels.
There are other design types for different purposes and each design will allow you to get the information you require with fewer experiments than a full factorial design, especially for larger numbers of factors.
When used correctly, DoE has the power to reveal the cause and effect relationship between factors and responses and deliver enhanced process understanding, while minimising experimental time and resource. The careful selection of the correct design type for your purpose will enable the efficient investigation and optimisation of your process. We are happy to support you to make the right choice for your needs.