Regular Two-Level Factorial Designs
The Regular Two-Level Factorial Design Builder offers two-level fullfactorial and regular fractional factorial designs. You can investigate 2 to 21factors using 4 to 512 runs. This collection of designs provides an effectivemeans for screening through many factors to find the critical few.
Full two-level factorial designs may be run for up to 9 factors. These designspermit estimation of all main effects and all interaction effects (except thoseconfounded with blocks.)
Stat-Ease offers a wide variety of fractional factorial designs.The software calculates detailed information about the alias structure when thedesign is built. This evaluation should be inspected to ensure the selecteddesign can cleanly estimate the interactions of interest.
Replicates: The value in this box is the number of times the requesteddesign will be produced. The number of runs in the final design is the number ofreplicates times the number of runs in the requested base design.
We do not recommend replicating a fractional factorial design.
Blocks: The value in this box is the number of pieces to break the designinto to account for known sources of variation. See Blockingfor more information.
When the number of blocks equals the number of replicates. The replicateddesigns will be in their own blocks.
Center points per block: When there are numeric factors, center points canbe added to check for curvature. The number entered here will be the number ofcenter points randomized within each block.
Show Generators: Checking this box brings up the advanced generatorsinterface when Next is clicked.
The roman numerals on this screen are the resolution. They are also color codedsuch that no color is a full factorial, red are Resolution III, yellow areresolution IV, and green are at least resolution V.
Red means Stop and Think: A resolution III design indicates that maineffects may be aliased with two factor interactions. Resolution III designs canbe misleading when significant two-factor interactions affect the response.
Yellow means Proceed with Caution: A resolution IV design indicates thatmain effects may be aliased with three-factor interactions. Two-factorinteractions may be aliased with other two-factor interactions. Resolution IVdesigns are a good choice for a screening design because the main effects willbe clear of two-factor interactions.
Green means Go Ahead: Resolution V (or higher) designs are just about asgood as a full factorial, while saving some runs. There is an assumption thatmain effects and two-factor interactions can adequately model the responsesurface.
Minimum Run, Resolution V Factorial Designs (Characterization)
These are a class of designs containing the minimum number of runs to estimateall main effects and all two-factor interactions (Resolution V) whilemaintaining treatment balance for each factor. If any of the runs are notcompleted (resulting in missing data) then the resulting design will beResolution IV.
Because they are minimum run designs, the power to detect small effects will belimited.
Because this is an irregular fraction, the significance of effects depends onthe other terms in the model. As terms are added to or taken away from the modelduring analysis, the ANOVA and model selection plots will change accordingly.
Irregular Rev V Fraction Design
These are two-level resolution V designs that use unusual fractions like 3/4,3/8, etc. of the number of runs that a full factorial would need. Thesefractional designs can fit a model that includes the linear and two-factorinteraction terms for all factors.
Because this is an irregular fraction, the significance of effects depends onthe other terms in the model. As terms are added to or taken away from the modelduring analysis, the ANOVA and model selection plots will change accordingly.
Minimum Run, Resolution IV Factorial Designs (Screening)
These designs allow all main effects to be estimated, clear of two-factorinteractions. The two-factor interactions will be aliased with each other. Likeall minimum run designs, they are extremely sensitive to missing data. Even onemissing data point will result in aliasing and cause the design to becomeResolution III. To protect against this possibility, the default option is toinclude two extra runs to protect against one botched run and improve the powerof the design.
Because they are minimum run designs, the power to detect small effects will belimited.
Because this is an irregular fraction, the significance of effects depends onthe other terms in the model. As terms are added to or taken away from the modelduring analysis, the ANOVA and model selection plots will change accordingly.
Plackett-Burman Design
This item generates a set of saturated screening designs based on thePlackett-Burman structures. Since these are generally run as Resolution IIIdesigns, you must assume the absence of interactions, otherwise you shouldchoose a higher resolution two-level factorial design. Plackett-Burman designsare useful for ruggedness testing (validation) where you hope to find little orno effect on the response due to any of the factors. Plackett-Burman designs arenot recommended for Screening when there is the possibility that two-factorinteractions exist. These interactions, if present, will bias the main effectestimates and can cause serious analysis problems.
Stat-Ease offers a selection of Plackett-Burman designs. The number offactors allowed is up to one less than the number of runs (for example 11factors in 12 runs.) Choose the design with the number of factors equal to orjust larger than the number you actually have. Fill in the factor names, units,type, and actual low and high levels. Factors can be specified as numerical orcategorical. If you have unused factors, leave them lettered, or name them dummy1, dummy 2, etc. Enter the response names and units.
If a “dummy” factor appears significant on the probability plot of effects, analiased interaction is likely the culprit.
Note
Plackett-Burman designs have extremely complex alias structures. UseONLY if your process doesn’t have interactions, or if you are doing ruggednesstesting and don’t expect to find significant effects.
Plackett-Burman (PB) designs are built “saturated” in Stat-Ease because anunsaturated PB creates interactions that are non-orthogonal to the main effects.This can cause serious problems in the alias structure, even to the extent thatpartial aliasing will occur with coefficients possibly greater than 1.0. Don’tdelete the dummy columns.
Taguchi Designs
Taguchi designs are a type of factorial design. Design options are availablewith differing numbers of factors and levels. Stat-Ease, Inc. encourages the useof standard Factorial, Multilevel Categoric, or optimal (custom) designs,because these may provide you with additional flexibility and a less complexalias structure. We do not recommend the use of Taguchi design given more moderndesign and analysis techniques.
To use the Taguchi designs, first pick the design you need from the pull-downlist. Then click on Next to inspect the alias structure for this design. Itis likely to be very complex. On the next screen, enter your response names.Then click on Next for the upfront power and then Finish to create thedesign layout.
Stat-Ease sets up saturated Taguchi designs. Use Taguchi’s lineargraphs (available in Taguchi textbooks) to determine which columns are used andwhich are eliminated from the analysis.
The analysis of Taguchi designs is done using standard analysis of variancetechniques.
Multilevel Categoric Design
The multilevel categoric (general factorial) design allows you to have factorsthat each have a different number of levels. It will create an experiment thatincludes all possible combinations of your factor levels. All factors should becategoric (i.e. batch type, tool type, process method) rather than numeric.
Note
If you have numeric factors, it may be more efficient to set up aresponse surface design with added categoric factors.
