pg_0024

Process Improvement

5.2.

Assumptions

5.2.3.

Is there a simple model.

Polynomial

approximation

models only

work for

smoothly

varying

outputs

In this chapter we restrict ourselves to the case for which the response

variable(s) are continuous outputs denoted as Y. Over the experimental

range, the outputs must not only be continuous, but also reasonably

smooth. A sharp falloff in Y values is likely to be missed by the

approximating polynomials that we use because these polynomials

assume a smoothly curving underlying response surface.

Piecewise

smoothness

requires

separate

experiments

If the surface under investigation is known to be only piecewise

smooth, then the experiments will have to be broken up into separate

experiments, each investigating the shape of the separate sections. A

surface that is known to be very jagged (i.e., non-smooth) will not be

successfully approximated by a smooth polynomial.

Examples of

piecewise

smooth and

jagged

responses

Piecewise Smooth Jagged

FIGURE 2.1 Examples of Piecewise

Smooth and Jagged Responses

5.2.3. Is there a simple model.

http://www.itl.nist.gov/div898/handbook/pri/section2/pri23.htm [5/7/2002 4:01:43 PM]