Plackett-Burman designs variables

Table 5.10. Plackett-Burman design matrix lor N 8 experiments and consequently m = 7 factors (including dummy variables) at two levels... 

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]. 

When all of the variables are quantitative, an estimate of the experimental error can be obtained by adding to the full factorial, fractional factorial or Plackett-Burman design, a number of runs at the center of the design. The center of the design is the midpoint between the low and high settings of the two-level factors in the experiment. Thus, if there are p variables, and the levels of the variables have been coded (-1, +1), then the center of the design is (Xj, = (0, 0,. .., 0). If the... 

B.S. Aswathan and VJ. Victor, Plackett-Burman design for effective screening of process variables, Indian Journal of Technology, 12 (1974) 367-369. 

The experimental setup for seven variables determining ultrasound bath-assisted enzymatic hydrolysis was optimised using a central composite design after a previous Plackett-Burman design... 

Hydride generation conditions were assessed by Plackett-Burman designs. Relevant variables were then optimised using a star central composite design... 

The effect of each variable in the ruggedness test is determined by the difference between the average high and low levels, as is done in the Plackett-Burman design. However, the Youden technique, as modified by Steiner, differs from the Plackett-Burman technique in that the Youden-Steiner experiment is performed in duplicate, and the standard error is estimated differently. An estimate of the experimental error is calculated by equation 5. ... 

The Plackett-Burman designs are convenient for fitting linear screening models when the number of variables is large and when it is desirable to keep the number of necessary runs to a minimum. One disadvantage is that the confounding patterns... 

The levels selected in a robustness test are different from those at which factors are evaluated in method optimization. For optimization purposes the variables are examined in a broad interval. In robustness testing the levels are much less distant. They represent the (somewhat exaggerated) variations in the values of the variables that could occur when a method is transferred. For instance, in optimization the levels for pH would be several units apart, while in robustness testing the difference could be 0.2 pH units. The levels can for instance be defined based on the uncertainty with which a factor level can be set and re.set 36 and usually they are situated around the method (nominal) conditions if the method specifies pH 4.0, the levels would be 3.9 and 4.1. The experimental designs used are in both situations the same and comprise fractional factorial and Plackett-Burman designs. 

The model used to assess the influence of the variables by a Plackett-Burman design is a linear model ... 

These relations can be used to determine the confoundings in Plackett-Burman designs. As an example to illustrate the principles, the design with seven variables in eight runs described on p. 182 is used. 

The above method must be used to elucidate the confounding pattern of Plackett-Burman designs. It is seen, that a fold-over design would separate the main effects from confounding with the two-variable interactions. A fold-over design would switch the signs of the Xj matrix and hence switch the signs of the alias matrix... 

With more than 15 variables, a Plackett-Burman design will reduce the number of experimental runs. 

A Plackett-Burman design may be the preferred choice if (a) a linear model is assumed to be satisfactory, (b) the number of variables is too high to permit the number of runs of a fractional factorial design. 

A twelve-run Plackett-Burman design can accomodate eleven variables. With 12 -15 variables, a fractional factorial design is better (confounding pattern can be analyzed). With more than 15 variables a Plackett-Burman is the preferred choice ... 

For studying such 24 kinetic parameters, Plackett-Burman design with 32 runs and 31 degrees of freedom was selected. The different parameters (variables) were prepared in two... 

We have already seen that had we wished to screen an 8th variable (the extruder grill diameter for example) we would have needed a Plackett-Burman design of 12 experiments. 

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