Modeling and Optimizing Analytical Methods

I asked a professor, visiting from a nation well regarded for its hardworking ethos, whether in his search for ever better catalysts for some synthesis or other, he used experimental design. His answer was, “I have many research students. They work very hard!” Many people believe that an infinite number of monkeys and typewriters would produce the works of Shakespeare, but these days few organizations have the luxury of great numbers of researchers tweaking processes at random in order to make them ever more efficient. The approach of experimental scientists is to systematically change aspects of a process until the results improve. In this chapter I look at this approach from a statistical viewpoint and show how a structured methodology, called experimental design, can save time and effort and arrive at the best (statistically defined) result. It may be a revelation to some readers that the tried-and-trusted “change one factor at a time” approach might yield incorrect results, after requiring more experiments than is necessary. In the sections that follow, I explain how experimental design entails more than just having an idea of what you are going to do before beginning an experiment. Optimization is the maximizing or minimizing a response by changing one or more input variables. In this chapter optimization is synonymous with maximization, as any minimization can be turned into a maximization by a straightforward transformation: Minimization of cost can be seen as maximization of profit; minimization of waste turns into maximization of production; minimization of f(x) is maximization of 1/f(x) or -f(x). Before describing methods of effecting such an optimization, the term optimization must be carefully defined, and what is being optimized must be clearly understood. There are some texts on experimental design available for chemists, although often the subject is treated, as it is here, within a broader context. A good starter for the basics of factorial designs is the Analytical Chemistry Open Learning series (Morgan 1991). Reasonably comprehensive coverage is given in Massart et al.’s (1997) two-volume series, and also in a book from the Royal Society of Chemistry (Mullins 2003).