Annals of the Institute of Statistical Mathematics

, Volume 39, Issue 3, pp 649–659

# On the robustness of balanced fractional 2m factorial designs of resolution 2l+1 in the presence of outliers

Article

## Summary

By use of the algebraic structure, we obtain a simplified expression for the outlier-insensitivity factor for balanced fractional 2m factorial (2m-BFF) designs of resolution 2l+1 derived from simple arrays (S-arrays), whose measure has been introduced by Ghosh and Kipnegeno (1985,J. Statist. Plann. Inference,11, 119–129). It is defined by use of the measure suggested by Box and Draper (1975,Biometrika, 62 (2), 347–352). As examples, we study the sensitivity ofA-optimal 2m-BFF designs of resolution VII (i.e.,l=3) given by Shirakura (1976,Ann. Statist.,4, 515–531; 1977,Hiroshima Math. J.,7, 217–285). We observe that these designs are robust in the sense that they have low sensitivities.

## Key words and phrages

Outliers sensitivities A-optimal designs projection matrices

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