Experimental Plackett-Burman

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. 

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... 

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]. 

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

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... 

A second change was made to the experimental order in that the initial experimental conditions were run first not last as recommended in the Plackett-Burman scheme. This is again a practical compromise as it allows the analyst to check the instrumental set-up with well-established conditions. 

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.

Spreadsheet 3.3. Data for the Rankit plot of interference effects in a cadmium biosensor determined from a Plackett-Burman experimental design. See figure 3.16 for the plot. 

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 ... 

Then, the particular experimental setup to prepare a set of calibration samples can be deployed following any of the procedures explained in Chapter 2 (experimental design and optimisation). We found it very useful to set a Plackett-Burman design at each level of the analyte concentration but, of course, other possibilities exist. The important point here is to obtain a sufficiently large number of calibration samples so that any (reasonable) combination of concomitants and analyte that might appear in the problem samples has been considered previously in the calibration. This is the general rule that "you should model first what you want to predict afterwards [18]. 

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... 

Construct a two-level Plackett-Burman experimental design [6] as illustrated in Table 13.1. Choose six metal ions for interference studies and include a dummy factor (one in which nothing is changed). 

Contrast coefficients for the Plackett-Burman experimental design used for interference studies. +1 represents high concentration and —1 represents low concentration of the interfering ions. All runs also contain the target metal ion... 

Fig. 13.3. Rankit plot for the cathodic OSWV copper peak current-density effects of interferents from a Plackett-Burman 7-factor experimental design. The effect is the change in the copper current density upon increasing the metal-ion interferent concentration from its low level (—1, 0.2 pM) to its high level (+1, 5pM). Reprinted from Ref. [5], Copyright (2005) with permission from Elsevier.

A discussion of the Plackett-Burman and Youden-Steiner techniques is given below, along with a discussion of the experimental results from their application. 

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 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. 

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