Constructing Orthogonal Fractional Factorial Designs When Some Factor-Level Combinations Are Debarred

In a factorial experiment, certain combinations of factor levels may not be feasible in the sense that observations are not available under such combinations. If an orthogonal fractional factorial design contains such infeasible combinations, there will be missing data, and it may not be possible to augment the design without losing the property of orthogonality. Sometimes certain combinations may be operationally feasible, but they are ruled out for other reasons. This article studies the construction of orthogonal designs excluding such combinations. A modification of Franklin and Bailey's algorithm for selecting defining contrasts, which takes debarred combinations into account, is also presented.