An aberration criterion for conditional models

TL;DR

This paper extends conditional models to include two pairs of factors, providing new parametrizations, optimality conditions, and a catalog of minimum aberration designs, bridging conditional and traditional models for small-run experiments.

Contribution

It introduces an extension of conditional models to two pairs of factors, along with methods for identifying minimum aberration designs and connecting them to traditional models.

Findings

Catalog of 16-run minimum aberration designs provided

All designs for 5-12 factors are also minimum aberration under traditional models

Includes strategies for finding optimal designs under extended models

Abstract

Conditional models with one pair of conditional and conditioned factors in Mukerjee et al. (2017) are extended to two pairs in this paper. The extension includes the parametrization, effect hierarchy, sufficient conditions for universal optimality, aberration, complementary set theory and the strategy for finding minimum aberration designs. A catalog of 16-run minimum aberration designs under conditional models is provided. For five to twelve factors, all 16-run minimum aberration designs under conditional models are also minimum aberration under traditional models.