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A Statistical Design Consideration in Robotic Systems

The use of automated sample preparation machines requiring sequences of different samples distinguishable by strength, for example, or treatments, has raised the question of how the samples should be ordered in view of possible carryover effects. The use of serially balanced sequences is advocated in this context where the residual effect of each treatment occurs one or more times with the direct effect of every other treatment and possibly itself. Such designs permit the study of carryover effects as well as treatment effects concurrently, thus obviating the need to do separate studies for carryover and treatment effects. The designs given in this paper have minimum length. Several examples are illustrated and the analysis is sketched for these experiments.