Introduction to Box and Wilson (1951) On the Experimental Attainment of Optimum Conditions

Abstract

Imperial Chemical Industries (ICI) was one of the first companies to recognize the value of statisticians and they had several, spread over the various divisions. ICI Dyestuffs Division, in particular, had the good fortune and foresight to have George E.P. Box as its statistical head and K.B. Wilson as one of its chemists. Their cooperation in this particular study set the foundation for the entire present field of response surface methodology. A problem of great importance to a chemical company is that of finding optimal operating conditions for its processes. For example, what combination of input levels of temperature, pressure, reaction concentration, and so on delivers a process's maximum yield? Box and Wilson began their study by estimating first derivatives of a response surface, and moving up the unknown surface based on what their estimates showed. After early successes with laboratory-scale experiments on previously unexplored systems, they found, on the plant processes, that steepest ascent methods alone were unlikely to give much more improvement after a while. The presence of obvious interactions between inputs soon led to a study of curved surfaces and the realization that many of the surfaces that actually occured in practice were ridgelike ones, with multiple optima, affording choices in the experimental conditions that could be used. Several of the ideas and techniques now in common use originated in this paper. 1. Instead of attention being concentrated only on effects estimated by a factorial design, which permitted only some of the higher-order derivatives to be estimated, thought was given to the order of the Taylor's series approximation and all derivatives of a specified order were estimated instead. S. Kotz et al. (eds.), Breakthroughs in Statistics