Minimum breakdown two-level orthogonal main-effect plans

• Robust designs against missing data for two-level orthogonal main-effect plans are investigated.
• Theoretical results regarding the nearly saturated designs are developed.
• A catalogue of the maximally robust designs with practical run-sizes is provided.

A new class of robust designs against missing data, called the minimum breakdown designs, is proposed for two-level orthogonal main-effect plans. The minimum breakdown designs provide the highest probability to derive a non-singular residual design for estimating the grand mean and all the main effects, when a fraction of experimental data is unavailable. Some theoretical and computational results for characterizing the minimum breakdown designs are developed. In addition, a catalogue of the proposed designs with practical run-sizes is presented for multifactorial experiments.