CCD_original {AsymmetricSORDs}

Central Composite Designs (CCD) with original levels

Description

This function generates Central Composite Designs (CCD) with original levels along with coded levels for a given number of input factors (v). The CCD constitute combinations of factorial points, axial points and center points. Three types of CCDs can be generated using this function i.e. ccc or cci or ccf. "ccc" is for Central Composite Circumscribed designs, "cci" is for Central Composite Inscribed designs and "ccf" is for Central Composite Face Centered designs. It gives the randomized layout of the design along with the moment matrix and prediction variance.

Usage

CCD_original(v, type, min_L, max_L, randomization = FALSE, variance = FALSE)

Arguments

v

Number of input factors, v(>2)

type

Type of central composite design i.e. ccc or cci or ccf. "ccc" is for Central Composite Circumscribed designs, "cci" is for Central Composite Inscribed designs and "ccf" is for Central Composite Face Centered designs

min_L

A vector of minimum levels of the factors

max_L

A vector of maximum levels of the factors

randomization

It is for generating the randomized layout of the design. It takes either TRUE or FALSE and by default, it is set to FALSE

variance

This is for generating the moment matrix and prediction variance of the design based on a second order model. It gives unique prediction variance along with its frequencies. It takes either TRUE or FALSE and by default, it is set to FALSE

Value

Central Composite Designs (CCD) for a given number of input factors (v) with original levels

Note

Here, the factorial portion consists of 2^v (full factorial) combinations and there is no upper limit for the number of input factors,v (>2). To get a CCD with smaller runs, one may use fractional factorial (of resolution V) in place of full factorial.

References

1) G.E.P. Box and K.B. Wilson (1951)." On the experimental attainment of optimum conditions".

2) M. Hemavathi, Shashi Shekhar, Eldho Varghese, Seema Jaggi, Bikas Sinha & Nripes Kumar Mandal (2022)<DOI: 10.1080/03610926.2021.1944213>. "Theoretical developments in response surface designs: an informative review and further thoughts".

Examples

library(AsymmetricSORDs)
CCD_original(5,'ccc',c(10,15,20,25,30),c(15,20,25,30,35),FALSE,FALSE)