Multistratum response surface designs

Response surface designs are usually described as if the treatments have be en completely randomized to the experimental units. However, in practice th ere is often a structure to the units, implying the need for blocking. If, in addition, some factors are more difficult to vary between units than oth ers, a multistratum structure arises naturally. We present a general strate gy for constructing response surface designs in multistratum unit structure s. Designs are constructed stratum by stratum, starting in the highest stra tum. In each stratum a prespecified treatment set for the factors applied i n that stratum is arranged to be nearly orthogonal to the units in the high er strata, allowing-for all the effects that have to be estimated. Three ex amples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment se t. Finally, some practical considerations in randomization are discussed.