Abstract: In some experimental situations, there is a natural grouping of factors. Prior knowledge may indicate that active two-factor interactions only occur within groups of factors. Designs of variable resolution (Lin (2012)) were introduced for such situations. However, main effects from one group in a design of variable resolution may be aliased with non-negligible two-factor interactions from another group. In this article, we introduce robust designs of variable resolution which ensure main effects are robust to non-negligible interactions. Constructions are provided for a number of situations. Some existence results are given as well.

Key words and phrases: Alias, clear effect, fractional factorial design, Hadamard matrix, Kronecker product, orthogonal array, robustness.