Slope Rotatable Central Composite Designs of Second Type

Abstract

Central composite design (CCD) is the most commonly used fractional factorial design used in the response surface model. Kim [1] proposed second order rotatable designs (SORD) of second type using CCD, in which the positions of axial points are indicated by two numbers\(\left(a_{1}, a_{2}\right)\). Kim and\(K_{0}\) [2] introduced second order slope rotatable designs (SOSRD) of second type using CCD, in which the positions of axial points are indicated by two numbers \(\left(a_{1}, a_{2}\right)\). In this paper, second order slope rotatable central composite designs of second type with\(2 \leq n_{3} \leq 4\) (where \(n_{\text {s }}\) denotes the number of replications of axial points) are suggested for \(2 \leq \mathrm{v} \leq 17\) (v-stands for number of factors). It is observe that the value of level \(\mathrm{a}_{2}\) (taking \(\mathrm{a}_{1}=1\) ) for the axial points in CCD required for slope rotatability for second type is appreciably larger than the value required for SORD of second type using CCD. And also noted that if we replicate axial points \(\left(n_{9}\right)\)in SOSRD of second type using \(\mathrm{CCD}\) then the value of \(\mathrm{a}_{2}\) (taking \(\mathrm{a}_{1}=1\) ) is approximately nearer to\(\mathrm{SORD}\) value \(\mathrm{a}_{2}\) of second type using CCD.