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Keywords:

  • response surface designs;
  • slope estimation;
  • rotatability;
  • slope rotatability;
  • correlated errors;
  • robustness;
  • intra-class;
  • inter-class;
  • compound symmetry;
  • tri-diagonal;
  • autocorrelated structure

Abstract

Das (Calcutta Statist. Assoc. Bull. 2003; 54:57–70) initiated a study of slope rotatability over axial directions with correlated errors. General conditions for second-order slope rotatability over axial directions were derived when errors have a general correlated error structure.

In this paper, a class of multifactor designs for estimating the slope of second-order response surfaces is considered when errors in observations are correlated. General conditions for second-order slope rotatability over all directions have been derived assuming that errors in observations have a general correlated error structure. It has been derived that robust second-order rotatable designs are also robust slope rotatable over all directions. The class of robust slope-rotatable designs over all directions has been examined when errors in observations have the following variance–covariance structures: intra-class, inter-class, compound symmetry, tri-diagonal and autocorrelated structure. Copyright © 2006 John Wiley & Sons, Ltd.