Slope rotatability over all directions with correlated errors
Article first published online: 20 DEC 2006
Copyright © 2006 John Wiley & Sons, Ltd.
Applied Stochastic Models in Business and Industry
Special Issue: Business, Industry and Government (BIG) Statistics
Volume 22, Issue 5-6, pages 445–457, September - December 2006
How to Cite
Nath Das, R. and H. Park, S. (2006), Slope rotatability over all directions with correlated errors. Appl. Stochastic Models Bus. Ind., 22: 445–457. doi: 10.1002/asmb.655
- Issue published online: 20 DEC 2006
- Article first published online: 20 DEC 2006
- Manuscript Accepted: 28 JUN 2006
- Manuscript Revised: 25 APR 2006
- Manuscript Received: 30 JUN 2005
- Korean Science and Engineering Foundation. Grant Number: R01-2003-000-10220-0
- response surface designs;
- slope estimation;
- slope rotatability;
- correlated errors;
- compound symmetry;
- autocorrelated structure
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.