Ficure 1 
Ficure 2 
Ficures | and 2,—Geometry helps statisticians improve industrial products and processes, 
such as the hypothetical chemical process shown in the diagram in figure 1. Like a 
great many processes, it is hard to perfect because it responds in a very irregular way to 
changes in temperature and pressure. The statistician doesn’t have to know any chemi- 
cal theory to find out what temperature and pressure settings give the maximum yield— 
represented by the highest point on the ‘‘response surface.” Rather, he approaches the 
problem like a blind man trying to find the highest peak in an unfamiliar country. The 
drawing in figure 2 illustrates his procedure. He starts with arbitrary settings and varies 
them slightly so that he can determine yields at the corners of a small square on the 
surface. If one corner is significantly higher than the others, he starts over again at 
that point and varies the settings to explore another small square. Successive steps 
lead him higher and higher. As the diagram in figure 1 makes evident, he chould be 
misled by several topographic features—e.g., the small peak in the foreground, the ridge 
at the right, or the crest of the pass between the twin peaks in the rear. Such a response 
surface could just as well represent engine performance as fuel and carburetor adjustment 
vary, or any other measurable quantity. When there are many variables to consider, 
the geometry becomes more complicated, because the surface has as many dimensions 
as there are independent variables. 
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