Multistratum Response Surface Designs

• Published in: Technometrics Vol. 43; no. 1; pp. 25 - 33
• Main Authors: Trinca, Luzia A, Gilmour, Steven G
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01-02-2001; The American Society for Quality and The American Statistical Association; American Society for Quality
• Subjects: Block structure; Design analysis; Design efficiency; Design of experiments; Experiment design; Experimentation; Factorial design; Factorials; Industrial design; Industrial experimentation; Interchange algorithm; Parametric models; Proteins; Random allocation; Residual maximum likelihood (REML); Split-plot design; Weighted averages
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/00401700152404291

Response surface designs are usually described as if the treatments have been completely randomized to the experimental units. However, in practice there 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 others, a multistratum structure arises naturally. We present a general strategy for constructing response surface designs in multistratum unit structures. Designs are constructed stratum by stratum, starting in the highest stratum. In each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata, allowing for all the effects that have to be estimated. Three examples 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 set. Finally, some practical considerations in randomization are discussed.