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 analysis; using
the data from replicate l.
The required desig
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
Recall The F statistic:
n ( yi. y.) F0 MStrt MSE
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 estimates for the main factor eects assuming all interact
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 brackets following the standard
number, this means they are
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) What is the value of y ?
b) What is the value of y ?
c)
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 some feel for the techniques used. Later,
when more compli
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, 11.18, 11.19, 11.31
1
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, 1132 34 933 = 35
a) What is the value of y.?
Bsh'+?>l
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, 7.2, 7.9, 7.21
1
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?
The dening relation is C = AB (or, equivalently, I = ABC)
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 Oct 8. Please use this fax number: (610) 758-4886.
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 factors, A, and B. The results generalize pretty easily
IE 410 Midterm Exam Answers Fall 2003
Average = 78.4 90 | 7 5 3 2 2 1 1 80 | 9 8 8 6 6 6 5 5 3 0 70 | 9 9 9 6 5 5 60 | 4 4 2 0 50 | 2 40 | 3 30 | 7
Question 1 An experiment will be conducted to see if the priced offered by car dealers for a used ca
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 Company ships chemicals in Batches.
We suspect variation
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 few things you can try: 1. Box-Cox transform: Lambd
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: Or equivalently, define how false H0 should be for
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 factors, A, and B. The results generalize pretty easily
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 Oct 8. Please use this fax number: (610) 758-4886.
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: Or equivalently, define how false H0 should be for
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, 8.45, 8.47, 8.48
1
Chapter 11
Design & Analysis of Experiments
7E 2009 Montgomery
1
Text reference, Chapter 11
Primary focus of previous chapters is
factor screening
Two-level factorials, fractional factorials are
widely used
Objective of RSM is optimization
RSM dates
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 Two-Sample t-Test Works:
Use S and S to estimate and
2
1
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 Seq SS Adj SS Adj MS
F
P
2 580.500 580.500 290.250 60.
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 more than two levels of interest, or there are
several f
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 RCBD
Other blocking scenariosLatin square
designs
Chapter
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) What is the value of y ?
b) What is the value of y ?
c)
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 two-factor factorial with fixed effects
The ANOVA for f
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:
Time of booting computers (from power on to finish boo