STAT 742: Advanced Design and Analysis of Experiments
TwoLevel Designs
I. Review of Basic Concepts for Regular TwoLevel Fractional Factorial Designs
Review:
What is the maximum number of twolevel factors that we can include in 8 runs, if we
require th
Introduction to Robust Parameter Design
Wu and Hamada Chapter 11
Definitions:
Robust = insensitive to variation
Control factors: inputs of the design or the manufacturing process that can be set
Noise factors: (experimental) factors that are hard to co
Analysis of Symmetric Orthogonal Arrays with More than
Two Levels (Wu and Hamada Section 6.56)
The analysis options will be illustrated with the seat belt experiment from Chapter 6. Ask
for an OA(27,34,3) with levels 0,1,2 and then create the 9 interacti
Nonregular TwoLevel Designs
Read Wu and Hamada Chapter 8.18.4 and Chapter 9
Nonregular Designs and their strength
We will use the notation OA(N,2k,t) to denote an Nrun fraction of a 2k factorial with
strength t. Strength t means that the design project
Response Surface Methodology
Multiple Response Optimization
In most real industrial experiments, there is more than one response of interest. In STAT 642, we
talked about the method of overlaying contour plots. This works best when there are at most 3 des
Response Surface Experiments for the Mixture Problem
In this section, we will discuss the experimental designs and models that are used to investigate products which are a blend (or mix) of several ingredients.
A. Models
In mixture applications, the facto
Optimal Designs
We have briefly referred to Doptimal designs already this semester. Wu and Hamada
devote several pages to Doptimal design augmentation. Montgomery Chapter 11 also is
helpful.
Optimal designs are concerned with choosing a design that will
Response Surface Methodology
OneStep RSM
Onestep RSM is a novel method for exploring a response surface using only one design. This is in contrast to the common practice in response surface optimization, which,
is to use a sequential experimentation pro
Response Surface Methodology
Ridge Analysis
Steepest ascent says to maximize the fitted first order model over the set of x vectors at a fixed
distance from the origin. Recall that the analysis of a secondorder model gives a stationary point
that is a ma
Supersaturated Designs
Read Wu and Hamada, Chapter 9, Section 9.6
It is common for the beginning stage of experimentation to consist of an initial experiment
involving many factors. Such screening experiments often utilize twolevel strength two
orthogona
Cross vs. Single Array Robust Parameter Design Experiments
Wu and Hamada, Sections 11.611.8
Section 11.6 begins with a very important comment:
If N (=N1N2, the run size of a cross array) is large and the cost of running the experiment is
proportion to N,
Sequential (FollowUp) Experiments
One of the advantages of 2kp designs is that they permit so many alternatives for followup
experiments. Sequential experimentation has been a hallmark of good industrial experimentation
ever since Box and Wilsons On th
Analyzing TwoLevel Factorial & Fractional Factorial Designs
Normal Plots and HalfNormal Plots (Read Wu and Hamada Chapter 4, Section 8):
k
kp
A standard means of analyzing unreplicated 2 and 2 designs is to estimate a saturated
(or nearly saturated) mo
Resolution III 2
kp
Designs
Topics to explore: saturated main effects design, projection, complementary design,
Hadamard matrix, row coincidence matrix, isomorphism
A saturated main effects 2
kp
design assigns all n1 degrees of freedom for all k main
e
Resolution IV 2
kp
Designs
Topics to explore: even designs, even/odd designs, secondorder saturated designs, alias
length pattern
Even resolution IV designs:
A design is called even if all the words in the defining relation have an even number of
letter
Resolution V 2
kp
Designs
The following table gives the maximum number of factors for resolution III, IV, and V.
n=8
n=16
n=32
n=64
n=128
n=256
n=512
III
7
15
31
63
127
255
n1
IV
4
8
16
32
64
128
n/2
V

5
6
8
11
17
23
n=1024 General
32
41,65,
The growt
Response Surface Methodology
Wu and Hamada Chapter 10
In STAT 642, we talked about the following:
Steepest Ascent
Central Composite Designs
Second~order models
Canonical analysis of the matrix of secondorder coefﬁcients
Overview of Chapter 10:
oooolo
10