Randomization of the experimental trials (runs) protects against the effect of the so called “lurking variables”. A lurking variable is one that has important effect however it is not included in the experimental configuration. This is expected especially in the first steps of an experimental study when the effect of one or more significant variables might have been underestimated.

So in general it is necessary to randomize the experimental runs.

In addition it is as equally important to consider doing at least two replicates (repeat each experiment twice) and this way obtain an estimation of “pure error” which represents common cause variation of your experiments.

Since you have already four variables a suggestion would be to consider in the first step a half fraction design with two replicates where you can include your 3 center points. This configuration brings a total of 19 experimental runs in one block, randomized if possible.

as you mention, it seems possible to use the temperature as BLOCK, I advise you to calculate the number of replicates per treatment and block.

keep in mind that the temperature as BLOCK, information increases, reducing the error variance (SME)

Dear Carlos,

As far as i know nuisance factor can be accounted for using blocking while tempertaure is a main factor in the case. Can it be also blocked?

is very little information in your experiment to help, I require the research question and consider variables such as treatment, but if Temperature is important, then is better Factorial Design for to observe Interactions.

You can use Split-plot designs for response surface. By using this you can do your experiments using max (min or middle) together. But in a random way, e.g. all middle, all min, all max. If you use Split-Plot designs you can estimate the effect of Temperature and possible interactions of such factor with others.

Please find attached a document explaining Split-plot designs for many cases.

http://www.jmp.com/software/pdf/30612.pdf