Plackett-Burman Fractional Factorial Design
9. Plackett-Burman Design
Video 13 and Video 14 demonstrate the design of the Plackett-Burman fractional factorial design using MS Excel and Minitab, respectively.
The Plackett-Burman Fractional Factorial Design was developed in 1946 for screening a long list of variables/factors (Plackett & Burman, 1946). The design is only of resolution of three. Therefore, it uses the lowest number of experiments. In fact, for many designs, it uses a lower number of experiments than the regular fractional factorial design of an experiment without losing much of the advantages of the regular fractional factorial design, such as the projectivity property of the regular fractional factorial design. The Plackett-Burman design uses a simple algorithm to generate the design for any number of factors with the lowest possible runs in Table 18.
Table 18. Plackett-Burman Design Generator (Plackett & Burman, 1946)
The following steps can be taken to generate the design using the Plackett-Burman Generator. However, the Video 13 will be easier to follow to generate the design.
- Copy the relevant design generator below the first factor 1.
- The last generator number (zero (0) for this example) is the first number for the second factor
- The first number of the first factor is the second number of the second factor
- The second number of the first factor is the third number of the second factor
- The last standard order # 8 is the low-level of all factors used in the study
- Rest of the factors can be design following the same algorithm.
MS Excel File 2 provides the Placket-Burman Design up to 47 variables. Readers are welcome to download and use them.
MS Excel File 2. Table 18. Plackett-Burman Fractional Factorial Design to 47 Variables