Plackett-Burman designs experimental matrix

From preliminary assays, the experimental error was estimated as 2.50%, expressed as percentage recovery. Note that the complete factorial design is a 2 , requiring 128 runs, whereas the Plackett-Burman design needs only 8 runs to estimate the effects. The responses to the 8 runs corresponding to the design matrix in Table 2.6 were as follows ... 

Table 9 shows the experimental matrix for a Plackett-Burman Design with 11 variables and the response (compressibility, to be minimized). It can be seen that each column has 6 — and 6 -f , meaning that each variable will have one half of the experiments performed at the — level and one half of the experiments performed at the + level. Again, as in the Factorial Design, the effect of each variable will be easily computed by calculating the algebraic sum of the responses, each with the appropriate sign. This means that the effect of each variable will be derived from the comparison of the... 

Strictly speaking, it is not the experimental design that is a Hadamard design but the model matrix X. But this notation is now common and we will use it. In order to build this type of experimental design, it is advised to use the mode of generation proposed by Plackett and Burman (6), which we review here Knowing the number of factors k, we determine the minimum number of experiments needed to study a polynomial model of degree 1 = it + I. and we seek the... 

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