Plackett-Burman designs examples

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. 

The difference can be seen from the following example. If there are six factors, one can perform a Plackett-Burman design with 8 experiments, containing six real and one dummy factor. Another possibility would be to perform the twelve experiment design that would contain five dummies. 

These two case studies are good examples of ruggedness tests that focus on the type of data analysis described in Section 3.4.6 and where one prefers not to carry out a statistical analysis. They will be described in detail later in this book (Chapter 5). The factors are examined at three levels in reflected Plackett-Burman designs. From the results of the designs normalized effects, Ex(%), are calculated. No statistical... 

Similar problems occur when examining different column factors. As already mentioned before, one is able to examine only one of the three column factors at the same time in a design (see Section 3.4.2). Suppose for example that one would like to examine the factors batch and manufacturer , among other factors, in a Plackett-Burman design and that the design for seven factors described in Table 3.16 was selected. In this design each factor has two levels, e.g. factor A (= manufacturer) has a (+) level for column K and a (-) level for column L and factor B (= batch number) has a (+) level for batch Bj and a (-) level for batch B2. This... 

Projection properties of Plackett-Burman designs were studied by Lin and Draper (1991, 1992). Their computer searches examined all of the projections of small Plackett-Burman designs onto a few factors. For example, each of the 165 projections of the 12-run design of Table 2 onto three factors consists of... 

Screening. These types of experiments involve seeing which factors are important for the success of a process. An example may be the study of a chemical reaction, dependent on proportion of solvent, catalyst concentration, temperature, pH, stirring rate, etc. Typically 10 or more factors might be relevant. Which can be eliminated, and which should be studied in detail Approaches such as factorial or Plackett-Burman designs (Sections 2.3.1-2.3.3) are useful in this context. 

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. 

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. 

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. 

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. 

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

The construction of a design by a Hadamard matrix is simple. Plackett and Burman have determined how the first row in the design matrix should be constructed so that the remaining rows can be obtained by cyclic permutations of the first row. An example to show this is given below. For a given n there can be many different n xn matrices which are Hadamard matrices. The Plackett-Burman matrices are by no means the unique solutions. 

In the following example, concerning the determination of the content of active components in pharmaceutical formulations, robustness tests of HPLC methods by means of statistical experimental design (DoE) of the Plackett-Burman type are explained in more detail. 

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