Plackett-Burman design. See

Figure 3.16. Rankit plot of the effects of interferences on a cadmium biosensor, determined from a Plackett-Burman design. See spreadsheet 3.3 for data.

A number of software packages or expert systems for ruggedness testing has been developed. RES (commercialized under the name Shaiker ) is an expert system created by Van Leeuwen et al. [4,23] and has been validated and evaluated [42,43]. It uses fractional factorial and Plackett-Burman designs and allows to test the factors at two or three levels. The interpretation criteria used here are the predefined values (see Section 3.4.8). 

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... 

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. 

If this appears insufficient, the design may be replicated n times. The effects are then estimated with a precision of a/(nN), improved by a factor of V . This also has the advantage that the repeatability o may be estimated. Alternatively N could be increased by employing a larger Plackett-Burman design, or fractional factorial design, possibly carried out in stages, or blocks (1). It may be then be possible to estimate further effects (interactions), as we shall see in chapter 3. 

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). 

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. 

We see that this applies to the model matrices from factorial designs and fractional factorial designs these matrices are Hadamard matrices. It is possible to construct Hadamard matrices by other principles, and it was shown by Plackett and Burman[l] how such matrices can be obtained for zi = 4, 8, 12, 16, 20, 24, 28, 32,..., i.e. when n is a multiple of four. 

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