Saturated Plackett-Burman designs

We have just discussed designs with which we can study the influence of up to 7, 15, 31.2 - factors using 8, 16, 32.2 experimental nms. Another class of fractional factorial designs employs a total of 12, 20, 24, 28. runs to simultaneously investigate up to 11, 19, 23, 27. factors. With these designs, proposed by R.L. Plackett and J.P. Burman, it is possible to estimate all k = n-l main effects (where n represents the number of runs) with minimum variance (Plackett and Burman, 1946). Table 4.17 presents a Plackett-Burman design for n = 12. 

With a saturated design of n runs we can study up to n-1 factors, but it is advisable to choose a smaller number. The columns not used to set the factor levels then play the roles of inert factors and can be used to estimate the error associated with the contrasts. For Plackett-Burman 

Contrasts of the 2jy fraction as a function of the main and binary interactions of the 2 complete factorial, neglecting interactions involving more than two factors 

The Plackett-Burman saturated fractional design for studying 11 variables with 12 runs 

A disadvantage of Plackett-Burman designs is that the relations between the calculated contrasts and the effects of a complete factorial are quite complex. This makes it difficult to choose the additional runs necessary to unconfound the effects. 

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The relationship of saturated fractional factorial and Plackett-Burman designs. 

Using row and column operations, convert the following 7-factor Plackett-Burman design to the saturated fractional factorial design shown in Table 14.7. 

For this reason one prefers to apply an experimental design. In the literature a number of different designs are described, such as saturated fractional factorial designs and Plackett-Burman designs, full and fractional factorial designs, central composite designs and Box-Behnken designs [5]. 

The Plackett-Burman designs, as do the saturated fi actional factorial designs, only allow for estimating the main effects. One assumes that all interaction effects are negligible compared to main effects. 

A Plackett-Burman design with N experiments can examine up to N-1 factors. This is a difference with fractional factorial designs. Some saturated fractional factorial designs however contain also N-1 factors (e.g. the design of Table 3.14) but this is not always the case. The saturated design for 5 factors, for example, is the 2 design. In this design only 5 factors are examined in 8 experiments. 

Saturated Designs Plackett-Burman Designs. Use in Screening and Robustness Studies... 

The most important alternatives for the saturated fractional factorial designs are the Plackett-Burman designs. The number of experiments for these designs is a multiple of four. They too allow the evaluation of maximally N — 1 factors. This means that it is for instance possible to study 11 factors with 12 experiments which is not possible for the fractional factorial designs. An example is shown in Table 6.6. 

When studying a new process one does not know which factors are relevant and many possible factors may affect the response. In such a case, the first step is to screen the candidate factors to select those that are relevant. Therefore the smallest possible fraction of a two-level design (a saturated fractional factorial design) or the related Plackett-Burman designs can be used (see Section 2.2.5.2). 

Plackett-Burman designs. In fractional factorial designs the number of experiments is 2 . For some situations, however, this is not convenient. Suppose for instance that one wants to study 19 factors. The saturated fractional factorial... 

Plackett-Burman and saturated fractional factorial designs. 

The Taguchi design for 12 runs, L12, is quite different from the Plackett-Burman saturated design to study 11 factors in 12 runs (Table 4.17). Even so, the two designs are orthogonal and should present similar results, if aU interaction effects are negligible. If this does not happen, the interpretations of the contrasts can be different, because the relations between the contrasts and the main and interaction effects are... 

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