by K. A. CHATTO and R. W. KENNARD, 1
Ε. I. du Pont de Nemours & Co., Inc. Evolutionary Operation in Plant-Scale Experiments
The Simplified Concepts EVOP is a different approach to process improvement. It applies sound, well tested principles to an area where experimenters encounter more than usual re straints
O O M E O F T H E considerations n e e d e d
in utilizing t h e concepts of E V O P are highlighted in this report. T h e discussion, covering t h e middle ground between techniques a n d successful case histories, begins with the simplest statistical abstraction of a process. We shall call the process a box
I n general we cannot predict t h e exact value of y, b u t can predict only the fraction of time that it will b e in some interval, Ay. However, in almost all practical situations we assume that t h e probability dis tribution of t h e observations is at least partly unknown. W e are ignorant of some aspects of the situa tion; that is, we d o n o t know t h e characteristics of o u r process. I n t h e simplest case this a m o u n t s to assuming that t h e m e a n , Θ, is unknown. T h e observations pro vide information about t h e dis tribution from which they come. Therefore, they guide us in deter mining t h e value of ΘStatistical inference is concerned with methods of using observations on t h e o u t p u t to obtain informa tion about t h e probability distribu tion a n d t h e m e a n Θ- T h e case before us n o w is too simple to con sider further, b u t it does provide the base to introduce a further degree of complexity.
T h e purpose of a n y experimentation is to learn something a b o u t t h e function,/. Therefore, What we want to learn about the proc ess, that is how it responds to controls X i and X 2 , can take various forms
How does output y compare with a postulated value, say θ = f (Xi = 10, X2 = 20) = 20?
The process is not a tightly sealed box. It has external leads, X x andX 2 , by which its characteristics can be changed O p e r a t i o n of t h e process produces an output, y, which for our purposes is a set of d a t a or observations, as we call them—i.e., values of Y, (yi,y2-..). W e assume t h a t t h e o b servations a r e values of a r a n d o m variable; in other words, t h e values cannot b e forecast exactly, b u t only within t h e confines of a probability distribution. A simple model is that of a normal dis tribution with mean θ and variance σ2
What is the range of operation for con trols Xi and X2? What is the extent of the nonshaded area? In the shaded area, the process may be inoper able—e.g., no reaction, or fouling, or plugging
These external leads a r e factors such as temperatures, concentrations, a n d rates which a r e u n d e r o u r con trol. W e postulate t h a t t h r o u g h these external controls we can change the characteristics of t h e process. T h a t is we c a n change t h e values of the output. Mathematically, we say t h a t we can change t h e value of θ by changing t h e values of X\ and X
