Function to support estimability requests for compromise designs
Addelman (1962) and Ke and Wu (2005) discuss compromise plans of different types. Their creation is supported by the function compromise.
overall number of factors
vector with indices of factors in group G1 (cf. details)
class of compromise designs that is to be generated; 1, 2, 3, or 4, cf. details below
logical stating whether the
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
Value is a list of the four components
minnrun.clear. The last two components are purely imformative,
while the first two provide input parameters for function
requirement can be used for specifying the required 2fis in the
perms.full can be used in the
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).
Addelman, S. (1962). Symmetrical and asymmetrical fractional factorial plans. Technometrics 4, 47-58.
Gr\"omping, U. (2010). Creating clear designs: a graph-based algorithm and a catalogue of clear compromise plans. Reports in Mathematics, Physics and Chemistry, report 05/2010, Department II, Beuth University of Applied Sciences Berlin. (Preprint for IIE Transactions; IIE Transactions is available at http://www.tandfonline.com.)
Ke, W., Tang, B. and Wu, H. (2005). Compromise plans with clear two-factor interactions. Statistica Sinica 15, 709-715.
FrF2 for creation of regular fractional factorial designs
as well as
for statistical and algorithmic information on estimability of 2-factor interactions
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
## 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$requirement ## Not run: ########## usage of estimable ########################### ## design with with BD clear in 16 runs FrF2(16,7,estimable = C1$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 ## End(Not run)
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