Slope Rotatable Designs Research Articles

Slope-Rotatability of Second Order Response Surface Regression Models with Correlated Error

In Das [8], a study of slope rotatable designs with correlated error was initiated and second order slope-rotatability conditions over axial directions were derived for a general correlated error structure. In this article a class of multifactor designs for estimating the slope of a second order response surface regression model with correlated error is considered. Second order slope-rotatability over all directions and also with equal maximum directional variance in the case of two factors have been derived for a general correlated error structure. In the process, some measures have been proposed for robust slope-rotatability over axial directions, over all directions and with equal maximum directional variance, and are illustrated with examples.

On the Efficiencies of Second Order Response Surface Designs for the Estimation of Responses and Slopes Using Symmetrical Unequal Block Arrangements with Two Unequal Block Sizes

In this paper, the efficiencies of various second order response surface designs, like second order rotatable designs (SORD), second order slope rotatable designs (SOSRD), SORDs with an equi-spaced doses design, and SOSRDs with an equispaced doses design using symmetrical unequal block arrangements (SUBA) with two unequal block sizes, are studied for the estimation of responses and slopes at different points (central, axial, cube corner points) on second order response surface designs. The study is done because in some cases a SORD, and SOSRD constructed by using a SUBA with two unequal block sizes have fewer design points compared to those constructed by other methods.

Modified second-order slope rotatable designs with equi-spaced levels

In this paper, a new method of construction of modified second-order slope rotatable designs with equi-spaced levels using central composite designs and balanced incomplete block designs is suggested.

Modified Second Order Slope Rotatable Designs using Symmetrical Unequal Block Arrangements with two Unequal Block Sizes

In this paper, a new method of construction of modified second order slope rotatable designs using symmetrical unequal block arrangements with two unequal sizes are constructed.

Slope-rotatable designs with equal maximum directional variance for second order response surface models

The concept of sloperotaiability with equal maximum directional vari ance for second order response surface models is introduced as a new design property. This requires that the maximum variance of the estimated slope over all possible directions be only a function of p, which is the distance from the design originif is shown that a rotatable design satisfies this property Also, minimization of tiie maximum variance of the estimated slope over all possible directions is proposed as a new design optirnality criterion, and op¬timal designs are called slope-directional minirnax designs. For the class of cquiradial designs, the slope-directional minirnax designs are compared with D— optimal designs.

A note on second order slope rotatable designs over all directions

Hader and Park (1978) introduced second order slope rotatability in axial directions. Park (1987) introduced second order slope rotatabilty over all directions. It is shown that these designs have the additional properly that the sum of the variances of estimates of slopes in all directions at any point is a function of the distance of the point from the design origin.

Construction of second order slope rotatable designs through balanced incomplete block designs

In this paper a new method of construction of second order slope rotatable designs (SOSRDs) through balanced incomplete block designs is suggested. In this method the number of design points required is in some cases less than the number required in Hader and Park slope rotatable central composite design (SRCCD)