Fractional—factorial screening

For the PS case, a three-variable Box-Behnken response surface methodology (RSM) design using formulation variables has been carried out. For the RF system, an eight-variable fractional-factorial screening study was done first to select significant factors, and this was followed by two RSM s which were similar in design to the one done for PS. The results have led directly to substantial improvements in both materials. 

Table 2. Fractional-factorial screening design for RF foams...

Assume that a 2 fractional factorial screening experiment has been run with seven variables, and where the "extra" variables have been defined as 4 = 12,... 

Fractional factorial (screening), Central composite (optimization)... 

Fractional factorial design is especially useful in case of a high number of influence variables from which the insignificant one have to be screened. 

Most screening designs are based on saturated fractional factorial designs. The firactional factorial designs in Section 14.8 are said to be saturated by the first-order factor effects (parameters) in the four-parameter model (Equation 14.27). In other words, the efficiency E = p/f = 4/4 = 1.0. It would be nice if there were 100% efficient fractional factorial designs for any number of factors, but the algebra doesn t work out that way. 

As an example of the use of dummy factors with saturated fractional factorial designs, suppose there are 11 factors to be screened. Just add four dummy factors and... 

Now suppose there are 16 factors to be screened. We would have to add 15 dummy factors and use the 2 " saturated fractional factorial design, but this would give an efficiency of only 17/32 = 53%. This is not very efficient. Most researchers would rather eliminate one of their original 16 factors to give only 15 factors. There is a saturated fractional factorial design that will allow these factors to be screened in only 16 experiments. 

The fractional factorial designs, including the Latin squares, are generally used for screening possible experimental variables in order to find which are the most important for further study. Their use is subject to some fairly severe assumptions which should be known and taken into consideration when interpreting the data ... 

Screening Experiments with 2 q Fractional Factorial Designs... 

The sparsity of effects principle (see Box and Meyer, 1986) makes resolution III and IV fractional factorial designs particularly effective for factor screening. This principle states that, when many factors are studied in a factorial experiment, the system tends to be dominated by the main effects of some of the factors and a relatively small number of two-factor interactions. Thus resolution IV designs with main effects clear of two-factor interactions are very effective as screening... 

In Section 5, we introduced the dyestuffs experiment to illustrate the methods for screening for dispersion effects in unreplicated fractional factorial experiments. Typically we anticipate that smaller experiments will be used for screening. So, in this section, we analyze two sets of 16 runs that are extracted from the dyestuffs experiment and which constitute fractional factorials more typical of the actual size of screening experiments. 

Supersaturated designs, and likewise grouping screening designs, provide very little information about the effects of the factors studied, unless they are followed up with further experiments. If it is possible to use a fractional factorial design... 

Andres, T. H. and Hajas, W.C. (1993). Using iterated fractional factorial design to screen parameters in sensitivity analysis of a probabilistic risk assessment model. Proceedings of the Joint International Conference on Mathematical Models and Supercomputing in... 

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