ccd.augment {DoE.wrapper}R Documentation

Functions for accessing central composite designs from package rsm

Description

Functions for accessing central composite designs from package rsm, and for augmenting existing fractional factorials in case of a late decision for a frequential procedure.

Usage

ccd.augment(cube, ncenter = 4, columns="all", block.name="Block.ccd",
        alpha = "orthogonal", randomize=TRUE, seed=NULL, ...)

Arguments

cube design generated by function FrF2. The design must not be a split-plot design, nor a parameter design in long version.
ncenter integer number of center points for each cube or star point block, or vector with two numbers, the first for the cube and the second for the star portion of the design
block.name name of block factor that distinguishes (at least) between blocks; even for unblocked cubes, the ccd design has a cube and a star point block
alpha “orthogonal”, “rotatable”, or a number that indicates the position of the star points; the number 1 would create a face-centered design.
randomize logical that indicates whether or not randomization should occur
seed NULL or a vector of two integer seeds for random number generation in randomization
... reserved for future usage
columns not yet implemented; it is intended to later allow to add star points for only some factors of a design (after eliminating the others as unimportant in a sequential process), and columns will be used to indicate those

Details

The statistical background of central composite designs is briefly described under CentralCompositeDesigns.

Function ccd.augment augments an existing 2-level fractional factorial that should already have been run with center points and should have resolution V.

In exceptional situations, it may be useful to base a ccd on a resolution IV design that allows estimation of all 2-factor interactions of interest. Thus, it can be interesting to apply function ccd.augment to a cube based on the estimable functionality of function FrF2 in cases where a resolution V cube is not feasible. Of course, this does not allow to estimate the aliased 2-factor interactions and therefore generates a warning.

Value

The function returns a data frame of S3 class design with attributes attached. The data frame itself is in the original data scale. The data frame desnum attached as attribute desnum is the original data frame returned by package rsm. The attribute design.info is a list of various design properties. The element type of that list is the character string ccd. Besides the elements present in all class design objects, there are the elements quantitative (vector with nfactor TRUE entries), and a codings element usable in the coding functions available in the rsm package, e.g. coded.data.
Note that the row names and the standard order column in the run.order attribute of ccd designs based on estimability requirements (cf. also the details section) are not in conventional order and should not be used as the basis for any calculations. The same is true for blocked designs, if the blocking routine blockpick.big was used.

Note

This package is currently under intensive development. Substantial changes are to be expected in the near future.

Author(s)

Ulrike Groemping

References

Box, G.E.P., Hunter, J.S. and Hunter, W.G. (2005, 2nd ed.). Statistics for Experimenters. Wiley, New York.

Box, G.E.P. and Wilson, K.B. (1951). On the Experimental Attainment of Optimum Conditions. J. Royal Statistical Society, B13, 1-45.

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/pri/section3/pri3361.htm, accessed August 20th, 2009.

Myers, R.H., Montgomery, D.C. and Anderson-Cook, C.M. (2009). Response Surface Methodology. Process and Product Optimization Using Designed Experiments. Wiley, New York.

See Also

See also ccd.design, FrF2, lhs-package, rsm

Examples

  ## purely technical examples for the sequential design creation process
    ## start with a fractional factorial with center points
    plan <- FrF2(16,5,default.levels=c(10,30),ncenter=6)
    ## collect data and add them to the design
    y <- rexp(22)
    plan <- add.response(plan,y)
    ## assuming that an analysis has created the suspicion that a second order 
    ## model should be fitted (not to be expected for the above random numbers):
    plan.augmented <- ccd.augment(plan, ncenter=4)
    ## add new responses to the design
    y <- c(y, rexp(14))  ## append responses for the 14=5*2 + 4 star points
    r.plan.augmented <- add.response(plan.augmented, y, replace=TRUE)

  ## for info: how to analyse results from such a desgin
    lm.result <- lm(y~Block.ccd+(.-Block.ccd)^2+I(A^2)+I(B^2)+I(C^2)+I(D^2)+I(E^2), r.plan.augmented)
    summary(lm.result)
    ## analysis with function rsm
    rsm.result <- rsm(y~Block.ccd+SO(A,B,C,D,E), r.plan.augmented)
    summary(rsm.result)  ## provides more information than lm.result
    loftest(rsm.result)  ## separate lack of fit test
    ## graphical analysis 
    ## (NOTE: purely for demo purposes, the model is meaningless here)
    ## individual contour plot
    contour(rsm.result,B~A)
    ## several contour plots
    par(mfrow=c(1,2))
    contour(rsm.result,list(B~A, C~E))
    ## many contourplots, all pairs of some factors
    par(mfrow=c(2,3))
    contour(rsm.result,~A+B+C+D)

[Package DoE.wrapper version 0.6-2 Index]