2k-p fractional factorial designs vs Plackett-Burman designs (similarities and differences)

[#1]

Regarding the 2k-p fractional factorial designs (n= 4, 8, 16, 32, etc) & Plackett-Burman designs that are not a power of 2 (eg, n= 12, 20, 24, etc).

a. What is similar about these two types of designs especially regarding their balance and orthogonality properties?

b. What is the main difference between these two types of designs especially regarding 2 factor interactions?

I know the following:

2k-p fractional factorial design is only useful if we can be assured that the 2-way interactions are not important. If this is the case then we will find Resolution III designs to be very useful and efficient. 

Plackett-Burman designs exist for N = 12, 20, 24, 28, 36, 40, 44, 48, ...... any number which is divisible by four. These designs are similar to Resolution III designs, meaning we can estimate main effects clear of other main effects. Main effects are clear of each other but they are confounded with other higher interactions.

When we have a 2k-p design, we have an alias structure that confounds some factors with other factors.

Plackett-Burman designs have partial confounding, not complete confounding, with the 2-way and 3-way and higher interactions. Although they have this property that some effects are orthogonal they do not have the same structure allowing complete or orthogonal correlation with the other two way and higher order interactions.

Any advice will be greatly appreciated.

[#2 · Accepted solution]

JMP supports these older design methods but it does not promote them. The regular fractional factorial designs were developed in the 1930s and the irregular fractional factorial designs by the Plackett-Burman method was published in the 1946. The purpose of those designs was to support the analysis of economical experiments when the screening principles hold. These designs do not support a broader class of experiments. These older methods were also based on the best technology at the time for hand calculation of the design and the model estimates. Today we use the best technology available: computer algorithms for optimal solutions.

My advice is to learn to use custom design in JMP, in general for a broad class of experiments, and to learn to use definitive screening designs, in particular, for screening experiments.

Your questions about the older design methods are good. However, it would take a very long reply to answer all your questions and such a reply would, no doubt, raise many more questions. I suggest instead of such a discussion that you read one of these books:

• Peter Goos and Bradley Jones (2011) "Optimal Design of Experiments: A Case Study Approach," John Wiley & Sons (for a modern approach to design)
• Douglas Montgomery (2019) "Design and Analysis of Experiments, 9th edition," John Wiley & Sons (for a comprehensive coverage of classic design methods)
• Heath Rushing, Andrew Karl, and James Wisnowski (2013) "Design and Analysis of Experiments by Douglas Montgomery: A Supplement for Using JMP," SAS Press (NOTE: you need Montgomery's book (above) as this is only the companion, but very useful)
• Robert Mee (2009) "A Comprehensive Guide to Factorial Two-Level Experimentation," Springer (for excellent coverage of the regular and irregular fractional factorial designs)

There are many good textbooks about the statistical design of experiments that cover these topics. These suggestions are only a few of them.

[#3]

I would definitely recommend using the Customer DOE tool in JMP and creating an optimal DOE versus a fractional factorial or a Plackett-Burman.  There are many advantages including a reduction in factor confounding and DOE design flexibility.  You can design the experiment you need versus being constrained to a "classic" design.