5.
Process Improvement
5.5. Advanced topics 5.5.9. An EDA approach to experimental design 5.5.9.9. Cumulative residual standard deviation plot


Design table in original data units 
As for the mechanics of interpolation itself, consider a continuation of
the prior k = 2 factor experiment. Suppose temperature T
ranges from 300 to 350 and time t ranges from 20 to 30, and the
analyst can afford n = 4 runs. A 2^{2} full factorial
design is run. Forming the coded temperature as X_{1} and the
coded time as X_{2}, we have the usual:


Graphical representation  Graphically the design and data are as follows:  
Typical interpolation question 
As before, from the data, the prediction equation is


Predicting the response for the interpolated point 
The important next step is to convert the raw (in units of the
original factors T and t) interpolation point into a
coded (in units of X_{1} and X_{2}) interpolation point. From
the graph or otherwise, we note that a linear translation between
T and X_{1}, and between t and X_{2} yields
T = 350 => X_{1} = +1
 1 ? 0 +1 300 310 325 350which in turn implies that
t = 30 => X_{2} = +1
 1 0 ? +1 20 25 26 30thus


Graphical representation of response value for interpolated data point 
Thus
