Plackett-Burman and Taguchi Designs

Where the number of factors is fairly large, the constraint that the number of experiments must equal a power of 2 can be rather restrictive. Since the number of experiments must always exceed the number of factors, this would mean that 32 experiments are required for the study of 19 factors, and 64 experiments for the study of 43 factors. In order 

Plackett and Burman published their classical paper in 1946, which has been much cited by chemists. Their work originated from the need for war-time testing of components in equipment manufacture. A large number of factors influenced the quality of these components and efficient procedures were required for screening. They proposed a number of two level factorial designs, where the number of experiments is a multiple of four. Hence designs exist for 4, 8, 12, 16, 20, 24, etc., experiments. The number of experiments exceeds the number of factors, k, by one. 

One such design is given in Table 2.26 for 11 factors and 12 experiments and has various features. 

There are as many high as low levels of each factor over file 12 experiments, as would be expected. The most important property of file design, however, is orthogonality. Consider the relationship between factors 1 and 2. 

Only certain generators possess all these properties, so it is important to use only known generators. 

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