Transcript Introduction to Statistical Quality Control, 4th Edition

Chapter 13
Process Optimization with
Designed Experiments
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.
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.
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.
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:
y  0  1x1  2 x 2  ... k x k  
• If curvature is present in the system, then a model
such as the second-order model may be of use:
k
k
i 1
i 1
k
y   0   i x i   ii x i2     
i  j 2
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.
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.
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.]
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.
Introduction to Statistical Quality Control,
4th Edition