Premium
Slope rotatability over all directions with correlated errors
Author(s) -
Nath Das Rabindra,
H. Park Sung
Publication year - 2006
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.655
Subject(s) - diagonal , mathematics , class (philosophy) , autocorrelation , covariance , variance (accounting) , statistics , symmetry (geometry) , order (exchange) , geometry , computer science , accounting , finance , artificial intelligence , economics , business
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.