Two-Level Multifactor Experiment Designs for Detecting the Presence of Interactions

摘要

A design optimality criterion tr(L) - optimality is applied to the problem of designing two-level multifactor experiments to detect the presence of interactions among the controlled variables. Rules are given for constructing tr(L) - optimal foldover designs and tr(L) - optimal fractional factorial designs. Some results are given on the power of these designs for testing the hypothesis that there are no two-factor interactions. Modifications of the tr(L) - optimal designs to satisfy other experimental objectives (estimability of effects, detection of the presence of other nonlinear effects, estimation of the error variance) are suggested. Examples are given to demonstrate the application of these designs to (i) screening for interactions, and (ii) evaluating the first-order assumption in the sensitivity analysis of a computer code.