Dear Dr. Paulo Marcelo Avila Neto

I haven’t used PB  in my research because my parameters in the process are not as high as yours

I usually use Response Surface Method RSM in my researches and I use Minitab software for analyzing the data

I’ve looked at the Minitab Software for Plackett-Burman Design as a factorial design of course, and the Attached matrix is achieved from Minitab:

also you could use my papers in the field of RSM.

if I could help you in your research I will be happy. you could also be in touch with me. 

best Regards

Mahmoud Moradi

Assistant Professor in Department of Mechanical Engineering, Malayer University

Thank You Dr Mahmoud Moradi. 

I do have minitab and I noticed it has the all negative run case  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

My problem is very deeper, because all the experiments already performed were done in Statistica using the table I attached. There is no way to go back and re-do all the experiments, specially because so many futher experiments, including several RSM DoE were followed after the PB. 

Now I was told the software table is somehow wrong. And I need references to justify why the PB in Statistica Software is wrong, or right. Is the wikipedia matrix also wrong? is the matrix on 

Hello Paulo,

The matrix you used is indeed the 16-runs PB design. Your design has the same properties as the ones found in the literature; that is, your design is orthogonal, it's a regular design, it has resolution 3, and the (partial) word length pattern is (A3, A4) = (35, 105). You can find out more about these properties in Mee, A Comprehensive Guide to Factorial Two-Level Experimentation, Springer, Chapter 6.

I didn't check the other matrices you provide but I presume they are the same 16-run PB design. The thing is that all the matrices are isomorphic, which means that you can arrive from one matrix to the other by relabelling the levels of the factors, permuting rows and/or permuting columns.There are many ways to check that two matrices are isomorphic. One quick though not the exact way to check that two matrices are isomorphic is by looking at their properties (as shown above). At the end of the day all that matters is that your design has good properties so you can detect the true effects that are driving the process under study.

Note that, the design you select from the catalogues is not the same you run in your experiment. You have to randomize the runs of the designs and also randomly assign the levels of your factors to the -1's and 1's, etc.

I hope it helps a bit,

A PB design is a res 3 design with partial aliasing of 2-way and higher interactions. 

Suppose that you have 10 factors to test and 16 runs to use. The PB design will actually have 15 columns to test 15 factors. Some software will give you columns 1 to 10, others 2 to 11, 3 to 12, 4 to 13, etc. All of them are PB designs. However, they will all look different. Further, some will use the original 1 to 15 design. Others will do odds then evens. So, 1 is still 1, column 2 is column 3, column 3 is columns 5, etc. As long as it has the properties, I would stick with that. That is all I would be worried about.