Modified Robust Second-Order Slope-Rotatable Designs

Abstract

Generally it is very difficult to construct robust slope-rotatable designs along axial directions. Present paper focuses on modified second-order slope-rotatable designs (SOSRDs) with correlated errors. Modified robust second-order slope-rotatability conditions are derived for a general variance–covariance structure of errors. These conditions get simplified for intraclass correlation structure. A few robust second-order slope-rotatable designs (over all directions, or with equal maximum directional variance slope, or D-optimal slope) are examined with respect to modified robust slope-rotatability. It is observed that robust second-order slope-rotatable designs over all directions, or with equal maximum directional variance slope, or D-optimal slope are not generally modified robust second-order slope-rotatable designs.

Keywords:

• Correlated errors
• Response surface designs
• Robust designs
• Robust modified slope-rotatability
• Robust slope-rotatability

Acknowledgment

The authors are very much indebted to two referees who have provided valuable comments to improve this paper.