FrF2 (version 2.3-3)

compromise: Function to support estimability requests for compromise designs

Description

Addelman (1962) and Ke and Wu (2005) discuss compromise plans of different types. Their creation is supported by the function compromise.

Usage

compromise(nfactors, G1, class=3, msg=TRUE)

Value

Value is a list of the four components perms.full, requirement,

class, and minnrun.clear. The last two components are purely imformative, while the first two provide input parameters for function FrF2.

requirement can be used for specifying the required 2fis in the estimable option, both with clear=FALSE and clear=TRUE. For clear=FALSE, perms.full can be used in the perms option for speeding up the search into a hopefully realistic time frame.

minnrun.clear indicates the minimum number of runs needed for a clear design.

Note that the catalogue catlg contains all designs needed for accomodating existing clear compromise designs in up to 128 runs (even minimum aberration among all existing clear compromise designs; for a catalogue of these, cf. Gr\"omping 2010).

Arguments

nfactors

overall number of factors

G1

vector with indices of factors in group G1 (cf. details)

class

class of compromise designs that is to be generated; 1, 2, 3, or 4, cf. details below

msg

logical stating whether the minnruns.clear element of the result should be reported in a message

Author

Ulrike Groemping

Details

For compromise plans, the factors are decomposed into a group G1 and a group G2. The different classes of compromise plans require estimability of different subsets of 2fis in addition to main effects:

Class 1: all 2fis within group G1 are estimable
Class 2: all 2fis within group G1 are estimable, as well as all 2fis within group G2
Class 3: all 2fis within group G1 are estimable, as well as all 2fis between groups G1 and G2
Class 4: all 2fis between groups G1 and G2 are estimable

The function returns a list of four components (cf. section “Value”). They can be used as input for the function FrF2, if compromise plans are to be created. Both distinct designs (Addelman 1962) and clear designs (Ke, Tang and Wu 2005) can be constructed, depending on the settings of option clear in function FrF2. More explanations on specifying estimability requirements for 2fis in general are provided under estimable.2fis.

References

Addelman, S. (1962). Symmetrical and asymmetrical fractional factorial plans. Technometrics 4, 47-58.

Groemping, U. (2012). Creating clear designs: a graph-based algorithm and a catalog of clear compromise plans. IIE Transactions 44, 988-1001. tools:::Rd_expr_doi("10.1080/0740817X.2012.654848"). Early preprint at http://www1.bht-berlin.de/FB_II/reports/Report-2010-005.pdf.

Ke, W., Tang, B. and Wu, H. (2005). Compromise plans with clear two-factor interactions. Statistica Sinica 15, 709-715.

See Also

See Also FrF2 for creation of regular fractional factorial designs as well as estimable.2fis for statistical and algorithmic information on estimability of 2-factor interactions

Examples

## seven factors two of which are in group G1
C1 <- compromise(7, c(2,4), class=1)
C1$perms.full  ## the same for all classes
C1$requirement
C2 <- compromise(7, c(2,4), class=2)
C2$requirement
C3 <- compromise(7, c(2,4), class=3)
C3$requirement
C4 <- compromise(7, c(2,4), class=4)
C4$requirement

if (FALSE) {
########## usage of estimable ###########################
  ## design with with BD clear in 16 runs
  FrF2(16,7,estimable = C1$requirement)
  ## design with BD estimable on a distinct column in 16 runs (any design will do,
  ##    if resolution IV!!!
  FrF2(16,7,estimable = C1$requirement, clear=FALSE, perms=C1$perms.full)
  ## all four classes, mostly clear, for 32 runs
  FrF2(32,7,estimable = C1$requirement)
  FrF2(32,7,estimable = C2$requirement)   ## requires resolution V
         ## as clear class 2 compromise designs do not exist due to Ke et al. 2005
  FrF2(32,7,estimable = C2$requirement, clear=FALSE, perms=C2$perms.full)
  FrF2(32,7,estimable = C3$requirement)
  FrF2(32,7,estimable = C4$requirement)
  ## two additional factors H and J that do not show up in the requirement set
  FrF2(32,9,estimable = C3$requirement)
  ## two additional factors H and J that do not show up in the requirement set
  FrF2(32,9,estimable = C3$requirement, clear=FALSE)
  ## note that this is not possible for distinct designs in case perms is needed,
  ## because perms must have nfactors columns
}