Experimentation order in factorial designs with 8 or 16 runs

Randomizing the order of experimentation in a factorial design does not always achieve the desired effect of neutralizing the influence of unknown factors. In fact, with some very reasonable assumptions, an important proportion of random orders afford the same degree of protection as that obtained by experimenting in the design matrix standard order. In addition, randomization can induce a big number of changes in factor levels and thus make experimentation expensive and difficult. This paper discusses this subject and suggests experimentation orders for designs with 8 or 16 runs that combine an excellent level of protection against the influence of unknown factors, with the minimum number of changes in factor levels.