Plackett-Burman designs are an alternative to fractional-factorial screening designs. Two-level fractional factorial designs must, by their nature, have a number of runs that are a power of two. Plackett-Burman designs exist for 12-, 24-, and 28-run designs.
Weld-Repaired Castings.jmp from the sample data folder uses a Plackett-Burman design, and is found in textbooks such as Giesbrecht and Gumpertz (2004) and Box, Hunter, and Hunter (1978). Seven factors are thought to be influential on weld quality. The seven factors include Initial Structure, Bead Size, Pressure Treatment, Heat Treatment, Cooling Rate, Polish, and Final Treatment. A Plackett-Burman design with 12 runs is used to investigate the importance of the seven factors. The response is . (There are also four terms that were used to model error that are not used in this analysis.)
Using the Screening platform, select the seven effects as X and Log Life as Y. (If terms are automatically populated in the Screening Platform launch window, remove the four error terms listed as effects.) Click OK. Screening Report for Weld-Repaired Castings.jmp appears, showing only a single significant effect.
Screening Report for Weld-Repaired Castings.jmp
Note asterisks mark four terms, indicating that they are not orthogonal to effects preceding them, and the obtained contrast value was after orthogonalization. So, they would not match corresponding regression estimates.
Supersaturated designs have more factors than runs. The objective is to determine which effects are active. They rely heavily on effect sparsity for their analysis, so the Screening platform is ideal for their analysis.
As an example, look at Supersaturated.jmp, from the sample data folder, a simulated data set with 18 factors but only 12 runs. Y is generated by
where ε ~ N(0,1). So, Y has been constructed with three active factors.
To detect the active factors, run the Screening platform with X1–X18 as X and Y as Y. The report shown in Screening Report for Supersaturated.jmp appears.
Screening Report for Supersaturated.jmp
Note that the three active factors have been highlighted. One other factor, X18, has also been highlighted. It shows in the Half Normal plot close to the blue line, indicating that it is close to the 0.1 cutoff significance value. The 0.1 critical value is generous in its selection of factors so you don’t miss those that are possibly active.
The contrasts of 5.1, –3, and 1.8 are close to their simulated values (5, –3, 2). However, the similarity of these values can be increased by using a regression model, without the effect of orthogonalization.
The p-values, while useful, are not entirely valid statistically, since they are based on a simulation that assumes orthogonal designs, which is not the case for supersaturated designs.