Question

An engineer wishes to maximize the output y of a water desalination facility by using Response Surface Methodology (RSM), y is measured on-line as parameters a, b, and c are tweaked. The following data are obtained:

a b c y
11 2.2 26 24.3
11 2.6 27 31.7
13 3.0 28 39.5
13 2.2 28 42.1
15 2.6 26 33.8
15 3.0 27 25.9
(a) Convert parameters a, b, and c to coded variables x1, x2, and x.
(b) Determine the vector of steepest ascent in terms of the coded variables.
(c) Which parameter has the most influence on output y?

Answer 1

a) Converting a, b and c to coded variables

X1 is defined for parameter a

X2 is defined for parameter b

X3 is defined for parameter c

`y = f(X_i)`

`y = f(X1,X2,X3)`

`y = \beta 0 +\beta 1X1 + \beta 2X2 +\beta 3X3` + ε

b) Vector of steepest ascent can be written as the formula attached.

c) The parameter 'a' has most influence on the output 'y'

`X1 = 2[(a - (amin + amax)/2) / (amax - amin)]\\X2 = 2[(b - (bmin + bmax)/2) / (bmax - bmin)]\\X3 = 2[(c - (cmin + cmax)/2) / (cmax - cmin)]`

Explanation:

Equation is (b)

Table is (c), use the equation to in (c) above to fill the table from A - AD