Package 'Vdgraph'

Title: Variance Dispersion Graphs and Fraction of Design Space Plots for Response Surface Designs
Description: Uses a modification of the published FORTRAN code in "A Computer Program for Generating Variance Dispersion Graphs" by G. Vining, Journal of Quality Technology, Vol. 25 No. 1 January 1993, to produce variance dispersion graphs. Also produces fraction of design space plots, and contains data frames for several minimal run response surface designs.
Authors: John Lawson <[email protected]>, with contributions from G. Vining
Maintainer: John Lawson <[email protected]>
License: GPL-2
Version: 2.2-7
Built: 2024-08-26 06:25:41 UTC
Source: CRAN

Help Index

This package creates variance dispersion graphs and fraction of design space plots for response surface designs

Description

The Vdgraph package provides functions for creating Variance Dispersion Graphs and Fraction of Design Space Plots of a standardized response surface design stored in a matrix or a data frame.

The function Vdgraph(des) creates the variance dispersion graph of the response surface design stored in the matrix or data frame des. The function FDSPlot(des) creates the fraction of design space plot of the response surface design stored in the matrix or data frame des. Useful response surface designs are also included as matricies in the package. These include the hexagonal design for two factors Hex2, the small composite designs for 3 to 6 factors and Roquemore's hybrid designs for 3 to 6 factors. The function Compare2Vdg makes the variance dispersion graphs of two designs on the same scale for comparison.

Details

Package: Vdgraph
Type: Package
Version: 2.2-7
Date: 2023-09-08
License: GPL2.0
Dependencies:
LazyLoad: yes
Packaged: 2023-09-08 19:54:07 UTC; Lawson
Built: R 3.0.2; i386-pc-mingw32; 2011-03-22 19:54:08 UTC; windows

Index: 

Compare2Vdg             this function makes Variance Dispersion Graphs
                        of two response surface designs on the same 
                        graph for comparison
Compare2FDS             this function makes fraction of design space 
                        plots of two response surface designs on the 
                        same graph for comparison
D310                    Roquemore (1976) Hybrid design D310
D311A                   Roquemore (1976) Hybrid design 311A
D311B                   Roquemore (1976) Hybrid design D311B
D416A                   Roquemore (1976) Hybrid design 416A
D416B                   Roquemore (1976) Hybrid design D416B
D416C                   Roquemore (1976) Hybrid design D416C
D628A                   Roquemore (1976) Hybrid design D628A
FDSPlot                 this function makses a fraction of design space 
                        plot of a response surface design
Hex2                    Hexagonal design for two factors
SCDDL5                  Draper and Lin's Small Composite Design for
                        five factors
SCDH2                   Hartley's Small Composite Design for two
                        factors
SCDH3                   Hartley's Small Composite Design for three
                        factors
SCDH4                   Hartley's Small Composite Design for four
                        factors
SCDH5                   Hartley's Small Composite Design for five
                        factors
SCDH6                   Hartley's Small Composite Design for six
                        factors
Vardsgr                 Loads compiled fortran in shared file vdg
Vdgraph                 this function makes a Variance Dispersion Graph
                        of a response surface design

Author(s)

John Lawson <[email protected]>

Maintainer: John Lawson <[email protected]>

This function compares Fraction of Design Space Plots for two response surface designs.

Description

This function compares Fraction of Design Space Plots for two response surface designs with the same number of factors over the unit hypercube design space.

Usage

Compare2FDS(des1, des2, name1, name2, mod=2)

Arguments

des1

des1 is a matrix or a data frame containing the first response surface design to be compared in coded or uncoded units. There should be one column for each factor in the design, and one row for each run in the design. The maximum number of rows allowed is 99, and the maximum number of columns is 7.
des2

des2 is a matrix or a data frame containing the second response surface design to be compared in coded or uncoded units. There should be one column for each factor in the design, and one row for each run in the design. The maximum number of rows allowed is 99, and the maximum number of columns is 7.
name1

name1 is a character string containing a descriptive name for the first design. This descriptive name should be no more than 40 characters in order to fit in the space for a legend. If left out name1 defaults to des1

name2

name2 is a character string containing a descriptive name for the second design. This descriptive name should be no more than 40 characters in order to fit in the space for a legend. If left out name2 defaults to des2

mod

mod is the model to be represented. 0 = linear model 1 = linear main effects plus linear by linear 2-factor interactions 2 = full quadratic response surface model (default.

Author(s)

John S. Lawson [email protected]

References

1.Zahran, A., Anderson-Cook, C. M. and Myers,R. H. "Fraction of Design Space to Assess Prediction Capability of Response Surface Designs" Journal of Quality Technology, Vol 35, No. 4, pp 377-386. 2003.

Examples

data(SCDH5)
data(SCDDL5)
Compare2FDS(SCDH5, SCDDL5, "Hartley SCD-5", "Draper-Lin SCD5", mod=2)

this function compares Variance Dispersion Graph of two response surface designs with the same number of factors on the same scale

Description

This function calls the function Vardsgr which uses Vining's (1993) fortran code to get the coordinates of a two variance dispersion graph, and then makes the plot.

Usage

Compare2Vdg(des,des2,name1,name2,ncolleg)

Arguments

des

des is a matrix or a data frame containing the first response surface design to be compared in coded or uncoded units. There should be one column for each factor in the design, and one row for each run in the design. The maximum number of rows allowed is 99, and the maximum number of columns is 7.
des2

des2 is a matrix or a data frame containing the second response surface design to be compared in coded or uncoded units. There should be one column for each factor in the design, and one row for each run in the design. The maximum number of rows allowed is 99, and the maximum number of columns is 7.
name1

name1 is a character string containing a descriptive name for the first design. This descriptive name should be no more than 40 characters in order to fit in the space for a legend. If left out name1 defaults to des

name2

name2 is a character string containing a descriptive name for the second design. This descriptive name should be no more than 40 characters in order to fit in the space for a legend. If left out name2 defaults to des2

ncolleg

The number of columns in the legend this can be 1 or 2

Value

vdgpl

vdgpl

This is a graph containing the two Variance Dispersion Graphs, one for each design

Note

This function calls the function Vardsgr to get the coordinates for the plot.

Author(s)

John S. Lawson [email protected]

References

1. Vining, G. "A Computer Program for Generating Variance Dispersion Graphs" Journal of Quality Technology, Vol 25, No. 1, pp. 45-58, 1993. 2. Vining, G. "Corrigenda" Journal of Quality Technology, Vol 25, No. 4, pp 333-335. 1993.

Examples

data(SCDH5)
data(SCDDL5)
Compare2Vdg(SCDH5,SCDDL5,"Hartley's SCD-5","Draper-Lin's SCD-5 fac",ncolleg=1)

Roquemore (1976) Hybrid design D310

Description

A This is an .rda file containing the design in a matrix.

Usage

data(D310)

Format

Three columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Roquemore (1976) Hybrid design 311A

Description

This is an .rda file containing the design in a matrix.

Usage

data(D311A)

Format

Three columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Roquemore (1976) Hybrid design D311B

Description

This is an .rda file containing the design in a matrix.

Usage

data(D311B)

Format

Three columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Roquemore (1976) Hybrid design 416A

Description

This is an .rda file containing the design in a matrix.

Usage

data(D416A)

Format

Four columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Roquemore (1976) Hybrid design D416B

Description

this is an .rda file containing the design in a matrix.

Usage

data(D416B)

Format

Four columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Roquemore (1976) Hybrid design D416C

Description

This is an .rda file containing the design in a matrix.

Usage

data(D416C)

Format

Three columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Roquemore (1976) Hybrid design D628A

Description

This is an .rda file containing the design in a matrix.

Usage

data(D628A)

Format

Three columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Calculate column means of design

Description

This function calculates means of design.

Usage

f(x)

Arguments

x

This is a design matrix

Value

mean

mean

This is the mean of the design x

Note

This function is called by the function Vdgraph.

Author(s)

John S. Lawson [email protected]

This function makes a Fraction of Design Space Plot of a response surface design.

Description

This function creates a Fraction of Design Space Plot over the hypercube design space from -1 to 1 on each component.

Usage

FDSPlot(des, mod=2)

Arguments

des

des is a matrix or a data frame containing a response surface design in coded or uncoded units. There should be one column for each factor in the design, and one row for each run in the design. The maximum number of rows allowed is 99, and the maximum number of columns is 7.
mod

mod is the model to be represented. 0 = linear model 1 = linear main effects plus linear by linear 2-factor interactions 2 = full quadratic response surface model (default.

Author(s)

John S. Lawson [email protected]

References

1.Zahran, A., Anderson-Cook, C. M. and Myers,R. H. "Fraction of Design Space to Assess Prediction Capability of Response Surface Designs" Journal of Quality Technology, Vol 35, No. 4, pp 377-386. 2003.

Examples

data(D310)
FDSPlot(D310)

Hexagonal design for two factors

Description

This is an .rda file containing the design in a matrix.

Usage

data(Hex2)

Format

Two columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Calculate column maximums of design

Description

This function calculates maximums of design.

Usage

mx(x)

Arguments

x

This is a design matrix

Value

mean

max

This is the maximum of the design x

Note

This function is called by the function FDSPlot.

Author(s)

John S. Lawson [email protected]

Draper and Lin's Small Composite Design for five factors

Description

This is an .rda file containing the design in a matrix.

Usage

data(SCDDL5)

Format

Five columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Hartley's Small Composite Design for two factors

Description

This is an .rda file containing the design in a matrix.

Usage

data(SCDH2)

Format

Two columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Hartley's Small Composite Design for three factors

Description

This is an .rda file containing the design in a matrix.

Usage

data(SCDH3)

Format

Three columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Hartley's Small Composite Design for four factors

Description

This is an .rda file containing the design in a matrix.

Usage

data(SCDH4)

Format

Four columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Hartley's Small Composite Design for five factors

Description

This is an .rda file containing the design in a matrix.

Usage

data(SCDH5)

Format

Five columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Hartley's Small Composite Design for six factors

Description

This is an .rda file containing the design in a matrix.

Usage

data(SCDH6)

Format

Six columns of independent variables

Source

source

References

Myers, R. H. and Montgomery D. C. Response Surface Methodology 2nd Ed., John Wiley and Sons NY, 2002. p.386

Loads compiled fortran in shared file vdg

Description

This function loads and runs the compiled fortran code vdg. vdg is Vining's 1999 JQT fortran code for producing variance dispersion graphs.

Usage

Vardsgr(ndpts, kvar1, kdv1, rdes)

Arguments

ndpts

This is the number of runs in the response surface design (maximum=99).
kvar1

This is the number of factors in the design matrix (maximum=6).
kdv1

This is the product of ndpts and kvar1.
rdes

This is the response surface design matrix stored as a vector of the concatenated columns of the design matrix, one column for each factor in the design.

Value

vdgr

vdgr

This is the matrix of coordinates for the variance dispersion graph. It is stored as a vector of concatenated columns. Each column is of length 20, and there are four columns in the matrix. The first column is the radius from the center of the response surface design. The second column is the maximum variance of a predicted value, the third column is the minimum variance of a predicted value, and the fourth column is the average variance of a predicted value.

Note

This function is called by the function Vdgraph.

Author(s)

John S. Lawson [email protected]

References

1. Vining, G. "A Computer Program for Generating Variance Dispersion Graphs" Journal of Quality Technology, Vol 25, No. 1, pp. 45-58, 1993. 2. Vining, G. "Corrigenda" Journal of Quality Technology, Vol 25, No. 4, pp 333-335. 1993.

this function makes a Variance Dispersion Graph of a response surface design

Description

This function calls the function Vardsgr which uses Vining's (1993) fortran code to get the coordinates of a variance dispersion graph, and then makes the plot.

Usage

Vdgraph(des)

Arguments

des

des is a matrix or a data frame containing a response surface design in coded or uncoded units. There should be one column for each factor in the design, and one row for each run in the design. The maximum number of rows allowed is 99, and the maximum number of columns is 7.

Value

vdgpl

vdgpl

This is a graph containing the Variance Dispersion Graph

Note

This function calls the function Vardsgr to get the coordinates for the plot.

Author(s)

John S. Lawson [email protected]

References

1. Vining, G. "A Computer Program for Generating Variance Dispersion Graphs" Journal of Quality Technology, Vol 25, No. 1, pp. 45-58, 1993. 2. Vining, G. "Corrigenda" Journal of Quality Technology, Vol 25, No. 4, pp 333-335. 1993.

Examples

data(D310)
Vdgraph(D310)