Assessing the bias in blocked two level fractional factorial designs with respect to confounding pattern
Blocked two-level fractional factorial designs are very useful in screening experiment and other areas of scientific research. In some experiments, apart from the main effects, some two-factor interactions may be important and should be estimated. Thus, the postulated model should include all main effects, some important two-factor interactions and blocking effects. The remaining two factor interaction and some other higher order interactions not included in the postulated model may confound and bias the estimate of the effects in the model which in turn lower the precision of the parameter estimate. It is therefore necessary to select an optimal design from the design space that will minimize this bias (contamination). In this article, two designs were selected with respect to confounding pattern and the bias accounted in the estimation of the regression coefficient of the postulated models were evaluated and compared. The confounding pattern of design I and II is (0, 6, 1) and (4, 2, 2) respectively; it was observed that bias accounted in the estimation of regression coefficient is higher in design II.
Keywords: Confounding Pattern, Defining Contrast Subgroup, Defining Words, Minimum Aberration, and Word-Length Pattern.
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