Experimental design Plackett-Burman designs

Keywords Experimental design Plackett-Burman design Factorial design Biotechnological process Acrylic acid Structured model... 

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... 

Using dummy factors in Plackett-Burman designs [24,26,27]. The effect of a dummy factor is considered to be due to experimental error. 

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 ... 

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... 

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. ... 

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

Ruggedness the capacity of an analytical method to remain unaffected and produce accurate data in spite of small but deliberately introduced changes in experimental conditions. Fractional factorial or Plackett Burman designs are frequently used to screen the impact of those changes. 

With 8 coefficients to be determined, we needed to do more than 8 experimental runs. The smallest screening design with a multiple of 4 experiments is a 12 experiment Hadamard (Plackett-Burman) design (table 2.6). Its derivation and structure is described in appendix II, along with the other 2-level Plackett-Burman designs. 

In the previous section we saw how factors at two levels may be screened using a Plackett-Burman design. In their paper (2), Plackett and Burman constructed experimental designs for factors at 2, 3, 5, and 7 levels. Such designs are termed symmetric, because all factors have the same number of levels. The designs may... 

The experimenter often chooses the smallest design consistent with his objectives and resources. Effects are estimated with a certain precision. For example, we have seen with the Plackett-Burman designs (and it is the same for the 2-level factorial designs of the following chapter) that the standard error of estimation of an effect is where ct is the experimental standard deviation (repeatability) and N is the number of experiments in the design. 

These are identical to the corresponding Plackett-Burman designs described in the previous section. They may be also be derived from the corresponding full factorial designs (resulting in a different standard order of experimentation). 

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. 

Table 1. Experimental variables at different levels used for the production of endoinulinase by G-60 using Plackett-Burman design. 

To obtain the best experimental conditions for plastic digestion, a 2 Plackett-Burman design for screening the significant factors and a 2 central composite design to optimise the significant experimental variables were carried out. 

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... 

Because of the complexities involved in understanding cause-effect relationships, an alternative approach to control the thin film microstructure has been pursued by some investigators—the use of statistically designed experiments to identify key processing parameters.114115 In these approaches, as illustrated in Table 2.6 for a Plackett-Burman screening study,114 limiting values for various experimental parameters are chosen. Films are then prepared from solutions synthesized under these conditions, and resulting film... 

TABLE 8 Example of a Plackett-Burman Experimental Design to Evaluate the Effect of varying Seven Conditions on Method Robustness... 

The second approach is to perform traditional pre-formulational studies using full factorial or Plackett Burman experimental designs [15]. Here, the preferred analytical methodology tends to be thermal and spectroscopic, rather than chromatographic, although the latter methodologies are still utilised. Differential scanning calorimetry (DSC), isothermal calorimetry (ITC) or Fourier-transform infrared (FT-IR) spectroscopy have all been utilised successfully. 

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 ruggedness of a method can be tested using two types of experimental designs. Procedure related factors at the one hand are examined mainly in screening designs of the Plackett-Burman or... 

The evaluation of robustness is normally considered during the development phase and depends on the type of procedure under study. Experimental design (e.g., fractional factorial design or Plackett-Burman design) is common and useful to investigate multiple parameters simultaneously. The result will help to identify critical parameters that will affect the performance of the method. Common method parameters that can affect the analytical procedure should be considered based on the analytical technique and properties of the samples ... 

Table 3.6. Seed contrast coefficients for Plackett-Burman experimental designs.

---