5.
Process Improvement
5.5. Advanced topics 5.5.3. How do you optimize a process? 5.5.3.1. Single response case


Optimal operating conditions may fall outside region where experiment conducted  Sometimes the optimal operating conditions x^{*} simply fall outside the region where the experiment was conducted. In these cases, constrained optimization techniques can be used to find the solution x^{*} that optimizes \( \hat{Y}(x) \) without leaving the region in the factor space where the experiment took place.  
Ridge analysis is a method for finding optimal factor settings that satisfy certain constraints 
"Ridge Analysis", as developed by
Hoerl (1959),
Hoerl (1964) and
Draper (1963), is an
optimization technique that finds factor settings
x^{*} such that they
\( \mbox{subject to} \hspace{.37in} x'x = \rho^{2} \) 

Solve with nonlinear programming software  The original formulation of Ridge Analysis was based on the eigenvalues of a stationarity system. With the wide availability of nonlinear programming codes, Ridge Analysis problems can be solved without recourse to eigenvalue analysis. 