Circuits for robust designs

TL;DR

This paper applies circuit theory to experimental design, providing detailed representations of design model kernels to analyze robustness, with examples from classical and factorial designs, and discusses software tools for complexity management.

Contribution

It introduces a circuit-theoretic approach to study the robustness of experimental designs, offering detailed kernel representations and software suggestions.

Findings

Circuit representations effectively analyze design robustness.

The approach applies to classical and factorial designs.

Software improvements can enhance analysis speed.

Abstract

This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix. This representation turns out to be an appropriate way to study the optimality criteria referred to as robustness: the sensitivity of the design to the removal of design points. Many examples are given, from classical combinatorial designs to two-level factorial design including interactions. The complexity of the circuit representations are useful because the large range of options they offer, but conversely require the use of dedicated software. Suggestions for speed improvement are made.