Package 'AsymmetricSORDs'

Asymmetric Second Order Rotatable Designs

Description

This function generates ASORDs through the orthogonal transformation of central composite designs as per the procedure given by J.S. Mehta and M.N. Das (1968). It would be providing two types of asymmetric designs for a given number of treatments (v). It requires four input parameters viz., v(>2); number_of_pairs(>0); z= vector of real number of length equals to number_of_pairs; type="ccc" or "cci" and randomization=TRUE or FALSE.

Usage

Asords(v, number_of_pairs, z, type, randomization = FALSE, variance = FALSE)

Arguments

v	Number of input factors, v(>2)
number_of_pairs	Number of pairs of input factors for which asymmetry is required
z	A vector of real number and its length equals to number_of_pairs
type	Type of central composite design i.e. ccc or cci. "ccc" is for Central Composite Circumscribed designs and "cci" is for Central Composite Inscribed designs
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

Asymmetric Second Order Rotatable Designs (ASORDs) for a given v.

References

1) J.S. Mehta and M.N. Das (1968)." Asymmetric rotatable designs and orthogonal transformations".

2)M. Hemavathi, Eldho Varghese, Shashi Shekhar & Seema Jaggi (2020)<DOI: 10.1080/02664763.2020.1864817>." Sequential asymmetric third order rotatable designs (SATORDs)".

3) 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)
Asords(5,2,c(2,3),"ccc",TRUE)

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Central Composite Designs (CCD) with coded levels

Description

This function generates Central Composite Designs (CCD) 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 CCD 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_coded(v, type, 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
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 coded 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_coded(5,'ccc',FALSE,FALSE)
CCD_coded(6,"cci",FALSE,FALSE)

---

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)

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Function for generating the moment matrix and variance of the predicted response

Description

This function generates the moment matrix and variance of the predicted response for a given design based on a second-order model, for measuring the rotatability of the design. The input should be the specified form of a design matrix with the coefficients of the corresponding input factors. A minimum number of centre points is to be used to ensure the non-singularity of X'X.

Usage

Pred.var(matrix)

Arguments

matrix

Design matrix with the coefficients of the corresponding input factors

Value

The moment matrix and the prediction variance for a given design based on a second-order model It gives unique prediction variance along with its frequencies.

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

## Not run: 
library(AsymmetricSORDs)
Pred.var(matrix)

## End(Not run)

---

Second Order Rotatable Designs with coded levels

Description

This function generates second order rotatable designs given in Das and Narasimham (1962) for a given number of input factors, v (3<=v<=16) with coded levels of the factors. It gives the randomized layout of the design along with the moment matrix and prediction variance. Here, all the factors are having 5-levels except for v=7, which gives a rotatable design with 3-levels for each factor.

Usage

SORD_coded(v, n0, randomization = FALSE, variance = FALSE)

Arguments

v	Number of input factors,v(3<=v<=16)
n0	Number of centre points, n0 (>0)
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

Second-Order Rotatable Designs with coded levels

References

1) M. N. Das and V. L. Narasimham (1962). "Construction of rotatable designs through balanced incomplete block designs".

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)
SORD_coded(4,3,FALSE,FALSE)

---

Second Order Rotatable Designs with original levels

Description

This function generates second order rotatable designs given in Das and Narasimham (1962) for a given number of input factors (3<=v<=16) with original levels along with coded levels of the factors. It gives the randomized layout of the design along with the moment matrix and prediction variance. Here, all the factors are having 5-levels except for v=7, which gives a rotatable design with 3-levels for each factor.

Usage

SORD_original(v, n0, min_L, max_L, randomization = FALSE, variance = FALSE)

Arguments

v	Number of input factors,v(3<=v<=16)
n0	Number of centre points,n0(>0)
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

Second-Order Rotatable Designs with original levels

References

1) M. N. Das and V. L. Narasimham (1962). "Construction of rotatable designs through balanced incomplete block designs".

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)
SORD_original(4,3,c(10,15,20,25),c(15,20,25,30),FALSE,FALSE)

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