Response Surface Designs for Crossed and Nested Multi-Stratum Structures

Response surface designs are usually described as being run under complete randomization of the treatment combinations to the experimental units. In practice, however, it is often necessary or beneficial to run them under some kind of restriction to the randomization, leading to multi-stratum designs. In particular, some factors are often hard to set, so they cannot have their levels reset for each experimental unit. This paper presents a general solution to designing response surface experiments in any multi-stratum structure made up of crossing and/or nesting of unit factors. A stratum-by-stratum approach to constructing designs using compound optimal design criteria is used and illustrated. It is shown that good designs can be found even for large experiments in complex structures.