1. Introduction to Statistical Quality Control, 4th Edition Chapter 13 Process Optimization with Designed Experiments

2. Introduction to Statistical Quality Control, 4th Edition Introduction Chapter 12 focused on factorial and fractional factorial designs. These designs are useful for factor screening (i.e., identifying important factors that affect the performance of a process) Once the appropriate process variables have been identified, the next step is usually process optimization.

3. Introduction to Statistical Quality Control, 4th Edition Introduction Process optimization is the procedure of finding the set of operating conditions for the process variables that result in the best process performance. Response surface methodology is an approach to optimization developed in the early 1950s.

4. Introduction to Statistical Quality Control, 4th Edition 13-1. Response Surface Methods and Designs Response surface methodology (RSM) is a collection of mathematical and statistical techniques that are useful for modeling and analysis in applications where a response is influenced by several variables. The objective of such an application is to optimize the response. In most RSM problems, the form of the relationship between the response and the independent variables is unknown. The first step in RSM is to find an approximation for the true relationship between the response, y, and the independent variables.

5. Introduction to Statistical Quality Control, 4th Edition 13-1. Response Surface Methods and Designs If the response is well modeled by a linear function of the independent variables, then the approximating function is the first-order model: If curvature is present in the system, then a model such as the second-order model may be of use:

6. Introduction to Statistical Quality Control, 4th Edition 13-1. Response Surface Methods and Designs RSM is a sequential procedure. The eventual objective of RSM is –to determine the optimum operating conditions for the system or –Determine a region of the factor space in which operating specifications are satisfied.

7. Introduction to Statistical Quality Control, 4th Edition 13-1. Response Surface Methods and Designs 13-1.1 The Method of Steepest Ascent Frequently, the initial estimate of the optimum operating conditions for a system will be far away from the actual optimum. The objective, then, is to move rapidly to the general vicinity of the optimum.

8. Introduction to Statistical Quality Control, 4th Edition 13-1. Response Surface Methods and Designs 13-1.1 The Method of Steepest Ascent The method of steepest ascent is a procedure moving sequentially along the path of steepest ascent. The path of steepest ascent can also be thought of as the direction of the maximum increase in the response. [Of course, if minimization is desired, follow the path of steepest descent.]

9. Introduction to Statistical Quality Control, 4th Edition 13-1. Response Surface Methods and Designs 13-1.1 The Method of Steepest Ascent Experiments are conducted along the path of steepest ascent until no further increase in response is observed (or until the desired response region is reached.) At that point, a new model my be fitted, a new direction of steepest ascent determined, or possibly further experiments conducted in that direction.