Experimental Designs Part 4 Varying Parameters to Expand the Design

Experimental Designs Part 4 - Varying Parameters to Expand the Design 

In Chapter 8, we looked at some experiments that involved two parameters (factors), each at two levels. In Chapter 10, we briefly looked at a three-factor, two-level design, with attention to how it could be represented geometrically. The use of the term three factor, two level to describe the design means that each factor was present at two levels, that is, the corresponding parameters were each permitted to assume two values. 

There are several ways we can expand a design such as this we can increase the number of factors, the number of levels of each factor, or we can do both, of course. There are other differences than can be superimposed over the basic idea of the simple, all-possible combinations of factors, such as to consider the effect of whether we can control the levels of the factors (if we can then do things that are not possible to do if we cannot control the levels of the factors), whether the levels correspond to physical characteristics that can be evaluated and the values described have real physical meaning (temperature, for example, has real physical meaning, while catalyst type does not, even though different catalysts in an experiment may all have different degrees of effectiveness, and reproducibly so). 

Another consideration is whether all the factors can be changed independently through their range of possible values, or whether there are limits on the possible values. The most obvious limiting situation is the case of mixtures, where all the components of a mixture must sum to 100%. Other limitations might be imposed by the physical (or chemical) behavior of the materials involved solubility as a function of temperature, for example, or as a function of other materials present (maximum solubility of salt in water-alcohol mixtures, for example, will vary with the ratio of the two solvents). Other limits might be set by practical considerations such as safety except for specialized work by scientists experienced in the field, few experimenters would want to work, for example, with materials at concentrations above their explosive limits. 

In Chapter 15, which was based on reference [1] we began our discussions of factorial designs. If we expand the basic n-factor two-level experiment by increasing the number of factors, maintaining the restriction of allowing each to assume only two values, then the number of experiments required is 2 , where n is the number of factors. Even for experiments that are easy to perform, this number quickly gets out of hand if eight different factors are of interest, the number of experiments needed to determine the effect of all possible combinations is 256, and this number increases exponentially. 

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