8.1. Suppose that in the chemical process development experiment in Problem 6.1 it was only possible
to run a one-half ﬁaction of the 24 design. Construct the design and perform the statistical analys
IE 410 Notes for Lecture 7 Today's topics are: Unequal sample sizes. Estimation of model parameters: o Least Squares o Estimable functions A start on Model Adequacy Checking
UNEQUAL SAMPLE SIZES What
Homework 2
The problem numbers are from the 8th edition of the textbook. If you
have the international version of 8th edition, do the problem with the number in brackets. If there is no number in brac
Midterm 14
1. Consider a single factor experiment with three levels of the factor and two replicates.
The response data turned out to be y11 = 20, y12 = 22, y21 = 24, y22 = 26, y31 = 28,
y32 = 30.
a)
Homework 1
In this homework, you will do the calculations (semi)-manually (i.e. using
something like Excel) to do the actual math but guring out what has to be
done yourself. This is for us to get som
Homework 5
The problem numbers are from the 8th edition of the textbook and may
be dierent from those in earlier editions or from the international version of
the 8th edition.
11.5, 11.6, 11.9, 11.12,
Midterm 15
1. Consider a single factor experiment with three levels of the factor and three replicates
The response data turned out to be yu 24, 3/12 = 22, yrs: 20 1121 27 y22_ m 26 y23 m 28,
931 = 32
Homework 3
The problem numbers are from the 8th edition of the textbook and may
be dierent from those in earlier editions or the international version of the
8th edition.
6.1, 6.5, 6.18, 6.26, 7.1, 7.
Final 12
1. In a factorial design with three factors, the following runs were performed: a = 10,
b = 12, c = 15, abc = 20.
a) What is the dening relation for this design and what is its resolution?
Th
Homework 4
The problem numbers are from the 8th edition of the textbook and may
be dierent from those in earlier editions or the international version of the
8th edition.
8.1, 8.9, 8.11, 8.18, 8.24, 8
ISE410 Final 2014
1. In a factorial design with four factors, the following runs were performed: d = 10,
ac = 12, b = 16, abcd = 20.
a) What is the full dening relation for this design?
b) Find the es
IE 410 Midterm Exam Fall 2003 Answer Sheet Instructions Exam is to be completed by Thursday, October 8. On campus students should hand in the exam then. Distance students can mail, e-mail, or fax on O
IE 410 Lecture 4 Details of the ANOVA In this lecture we will: Discuss power and the F stat Learn about SS and degrees of freedom Learn about decomposition of SS's Try to understand Cochran's theorem
IE 410 Lecture 21:
Nested and Hierarchical Designs
and
Rules for Expected Mean Squares
Two Stage Nested Designs
Consider the following: Example:
A Company deals with 3 suppliers of
chemicals.
Each Co
IE 410 Fall 2003 Final Exam Solutions Question 1. a) Examination of the residuals from the multifactor Anova clearly shows a problem. Could be an outlier, could be non-constant variance. There are a f
IE 410 Design of Experiments Lecture 16 Factorial Designs Continued
Sample Size: Both factors fixed. The basic procedure is the same: Specify a practically significant difference you want to detect:
IE 410: Design of Experiments Lecture 15: Factorial Experiments Well we have been hinting at, and preparing for multi-factor experiments for a while, finally they are here.
To start, assume two facto
IE 410 Midterm Exam Fall 2003 Answer Sheet Instructions Exam is to be completed by Thursday, October 8. On campus students should hand in the exam then. Distance students can mail, e-mail, or fax on O
IE 410 Design of Experiments Lecture 16 Factorial Designs Continued
Sample Size: Both factors fixed. The basic procedure is the same: Specify a practically significant difference you want to detect:
IE 410: Design of Experiments Lecture 15: Factorial Experiments Well we have been hinting at, and preparing for multi-factor experiments for a while, finally they are here.
To start, assume two facto
Steps in RSM
1. Find a suitable approximation for y = f(x) using LS
cfw_maybe a low order polynomial
2. Move towards the region of the optimum
3. When curvature is found find a new
approximation for y
Estimation of Parameters
1 n
y yi estimates the population mean
n i 1
n
1
2
2
S
( yi y ) estimates the variance
n 1 i 1
2
Chapter 2
Design & Analysis of Experiments 7E 2009
Montgomery
1
How the Tw
Attachment
13.4
(a)
Factor
Row
Column
Type
random
random
Levels
3
4
Values
1, 2, 3
1, 2, 3, 4
Analysis of Variance for Response, using Adjusted SS for Tests
Source
Row
Column
Row*Column
Error
Total
DF
Chapter 3
Design & Analysis of
Experiments 7E 2009
1
What If There Are More Than
Two Factor Levels?
The t-test does not directly apply
There are lots of practical situations where there are
either m
Design of Engineering Experiments
The Blocking Principle
Text Reference, Chapter 4
Blocking and nuisance factors
The randomized complete block design or
the RCBD
Extension of the ANOVA to the RCB
Midterm 12
1. Consider a single factor experiment with three levels of the factor and two replicates.
The response data turned out to be y11 = 10, y12 = 12, y21 = 14, y22 = 16, y31 = 18,
y32 = 20.
a)
Chapter 5
Design & Analysis of Experiments
7E 2009 Montgomery
1
Design of Engineering Experiments
Introduction to Factorials
Text reference, Chapter 5
General principles of factorial experiments
The
The Analysis of
Speed of Booting Computer
Abstract
Sixteen computers with different level of configuration:
Hard Drives - nuisance factor (Block)
CPU
Memory size
Operating System
Response variable:
Design of Engineering Experiments
Blocking & Confounding in the 2k
Text reference, Chapter 7
Blocking is a technique for dealing with
controllable nuisance variables
Two cases are considered
Repli