Split-plot designs have become increasingly popular in industrial experimentation because some of the factors under investigation are often hard-to-change. It is well-known that the resulting compound symmetric error structure not only affects estimation and inference procedures but also the efficiency of the experimental designs used. In this paper, we compute D-optimal first and second order split-plot designs and show that these designs, in many cases, outperform completely randomized designs in terms of D- and G-efficiency. This suggests that split-plot designs should be considered as an alternative to completely randomized designs even if running a completely randomized design is affordable.
Key Words: Design of Experiments; D-Optimality; G-Optimality; Split-Plot Designs.
By PETER GOOS and MARTINA VANDEBROEK, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000 Leuven, Belgium
SPLIT-PLOT designs (SPDs) are heavily used in industry, especially when factor levels are difficult or costly to change or control. Typical examples of such factors are pressure, humidity, and process temperature. Rather than conducting a completely randomized experiment in which pressure has to be adjusted according to the randomization scheme, it is often preferable, for example, to execute several consecutive experimental runs with the same setting for pressure. As another example, an experimenter can group all experimental runs with the same temperature level and execute them simultaneously in one furnace. In doing so, the number of changes in the levels of the hard-to-change factors is limited to the number of levels. Letsinger, Myers, and Lentner (1996) pointed out that the resulting compound symmetric error structure affects estimation and inference procedures as well as design efficiency. Ganju and Lucas (1999) argued that split-plot experiments should be designed rather than being the accidental outcome of a random run order. Goos and Vandebroek (2001b, 2003) proposed algorithms to construct D-optimal split-plot designs in this context. Trinca and Gilmour (2001) presented a method to construct multi-stratum designs, of which split-plot designs are a special case.
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