An investigator may possess information about certain characteristics of experimental units that can have a substantial effect on the response prior to running an experiment. It is observed as essential to take these characteristics into account when designing the experiment and when analyzing the resulting data. Designing of blocked experiments is considered where certain properties of the blocks have been measured using one or more categorical or quantitative variables, called covariates. Here, the experimenter is allowed to quantify the impact of the covariates on the response and also to estimate possible interactions between the covariates and the experimental factors. Two different methods have been proposed for generating optimal designs in the presence of additional information about the experimental units. While the first method fixes the number of runs performed on each experimental unit, the second method allows for varying numbers of runs applied to each experimental unit, subject to a constraint on the total number of runs. The paper discusses several illustrative examples using each method and presents a real-time experiment using previously fabricated batches of polypropylene as experimental units in a study on the effects of a subsequent plasma treatment.
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