The Construction of Trend-Free Run Orders of Two-Level Factorial Designs

原文摘要

In experimental situations where a factorial design with all factors occurring at two levels is to be run in a time sequence, the usual advice given to the experimenter is that the order of runs should be randomized before the experiment is performed; however, randomization may lead to an undesirable run order. For example, in a factory experiment, there may be a certain learning process that occurs over time as a result of making level changes in the factors being studied, or there may be equipment wear-out. In either case the observations obtained will be affected by uncontrollable variables that are highly correlated with the time or position in which they occur, and randomization may lead to a run order in which the estimates of factor effects are adversely effected by the presence of the trend. Joiner and Campbell (1976) gave some more specific examples as to when trend effects can occur in sequential experiments. Therefore, it is important to consider systematic designs in which the estimates for factor effects of interest are trend-resistant. This article constructs run orders of 2 n complete and 2 n—p fractional factorial designs in which the estimates of main effects and two-factor interactions are orthogonal to some polynomial trends. It is shown that in the standard order of a complete 2 n design, any k-factor interaction contrast is orthogonal to a (k – 1)-degree polynomial trend. Thus by designating some high-order interaction contrasts in the standard ordering as the desired effects or interaction contrasts, a run order can be derived in which these desired effects are orthogonal to high-degree polynomial trends. Symmetric block designs are shown to be useful for constructing such trend-free run orders of 2 n complete factorials. Run orders of fractional factorial designs are also considered. The concept of local trend resistance is defined, and it is shown that trend-free run orders also have the property of local trend resistance.

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