Plackett-Burman plan

The Plackett-Burmaa plan, which is based on statistics and combinatorial analysis, allows N— 1 effects of variables to be determined simultaneously in N tests. In this highly simplified test plan, only the main effects can be determined numerically at the same time, error estimation is performed by means of a blank variable. Interactions between the variables can not be determined. A test matrix for seven variables is shown in Table 13-11. 

To calculate the effects the measurements are added or subtracted with the signs listed in the columns, and the sum is divided by foiu. 

The blank effects should be zero. Usually the blank effects are regarded as the experimental error and are used to test the significance of the main effects. This is done by performing a 7-test the mean sum of squares of the blank effects is calculated as the variance (Eq. 13-16). 

The variance of an effect is determined by calculating the test quantity t = effect/s. 

An example is the identification of the significant reaction parameters in the bishy droformylation of 1,3-pentadiene (Table 13-12). The results of the hydroformyla-tion experiments are summarized in Table 13-13. The results were evaluated by the method described above (Table 13-14). 

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An example of a Plackett Burman plan for Z = 2 levels, m = 7 influence factors (including dummy variables) and, therefore, N = 8 runs is given in Table 5.10. 

Table 13-13 Plackett-Burman plan for the hydroformylation of 1,3-pentadiene ...

The experiments were carried out according to a Plackett-Burman plan. The results are summarized in the following matrix ... 

The most important alternative to the fractional factorial experimental plans are Plackett-Burman plans (31). With these, plans are now available that show similar characteristics to full and fractional factorial experimental plans in addition, they are definable for all multiples of4 (12, 20, 24,28,...), which are not power-of-two numbers. A disadvantage, as with the fractional factorial experimental plans, is that only a statistical resolution of 111 is given for these experimental plans this means that only main effects can be estimated. A mixing of main effects and interactions carmot easily be determined, since very few show an overlapping of a two-fold reciprocal effect with a main effect thus, misinterpretations can occur in practice [36]. Table 2 shows a Plackett-Burman experimental plan forn= 12. 

Due to the fact that it is more reasonable for the robustness test of an HP LC method to determine whether a method is robust in relation to small specific changes of the method parameters, instead of making statements about main effects and intreractions as well as their mixing, the Plackett-Burman plans are the most frequently applied experimental plans for the robustness test of an H P LC method. 

If nonlinear effects are expected the variables must be varied at more than two levels. A screening plan comparable to the Plackett Burman design but on three levels is that of Box and Behnken [I960]. 

Table 13-11 Plackett-Burman test plan with seven factors...

For the design of a Plackett-Burman experimental plan for less than 11 factors, the appropriate number of columns are omitted. 

For the determination of the influence of these six factors, a Plackett-Burman test plan with 12 experiments was chosen (Table 4). 

The influence of water components on the flame photometric determination of potassium and sodium can be detected by factorial experiments. By application of multifactorial plans according to PLACKETT and BURMAN the qualitative determination of the influence of various variables is possible with relatively few experiments [SCHEFFLER, 1986]. For mathematical fundamentals see Chapter 3. 

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