STAT 742: Advanced Design and Analysis of Experiments
Two-Level Designs
I. Review of Basic Concepts for Regular Two-Level Fractional Factorial Designs
Review:
What is the maximum number of two-level
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
No
Analysis of Symmetric Orthogonal Arrays with More than
Two Levels (Wu and Hamada Section 6.5-6)
The analysis options will be illustrated with the seat belt experiment from Chapter 6. Ask
for an OA(27,
Nonregular Two-Level Designs
Read Wu and Hamada Chapter 8.1-8.4 and Chapter 9
Nonregular Designs and their strength
We will use the notation OA(N,2k,t) to denote an N-run fraction of a 2k factorial wi
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 cont
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 in
Optimal Designs
We have briefly referred to D-optimal designs already this semester. Wu and Hamada
devote several pages to D-optimal design augmentation. Montgomery Chapter 11 also is
helpful.
Optimal
Response Surface Methodology
One-Step RSM
One-step 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 optimiza
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 s
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 exp
Cross vs. Single Array Robust Parameter Design Experiments
Wu and Hamada, Sections 11.6-11.8
Section 11.6 begins with a very important comment:
If N (=N1N2, the run size of a cross array) is large and
Sequential (Follow-Up) Experiments
One of the advantages of 2k-p designs is that they permit so many alternatives for follow-up
experiments. Sequential experimentation has been a hallmark of good indu
Analyzing Two-Level Factorial & Fractional Factorial Designs
Normal Plots and Half-Normal Plots (Read Wu and Hamada Chapter 4, Section 8):
k
k-p
A standard means of analyzing unreplicated 2 and 2 desi
Resolution III 2
k-p
Designs
Topics to explore: saturated main effects design, projection, complementary design,
Hadamard matrix, row coincidence matrix, isomorphism
A saturated main effects 2
k-p
des
Resolution IV 2
k-p
Designs
Topics to explore: even designs, even/odd designs, second-order saturated designs, alias
length pattern
Even resolution IV designs:
A design is called even if all the words
Resolution V 2
k-p
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
n-1
IV
4
8
16
32
64
128
n/
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 seco