Chapter 1.
Strategy and Competition
Forecasting and Inventory Example
Leading manufacturer of high-tech
equipment
Account team forecasts
Inaccurate forecasts led to huge levels of
inventory ($M of obsolete product)
MORE DETAILS
What went wrong?
What
Lecture 14
Normal
Random Variables
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Sections 4-6, 4-7
Copyright 2010 by
Normal RV
The normal distribution is key in statistics (subject of IE 361,
461)
The normal distribut
Lecture 13
Specific Continuous
Random Variables
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Sections 4-5, 4-8
Why look at some specific continuous
rvs?
For the same reasons as for the discrete case
We can develop so
Lecture 7
Introduction to
Continuous Random Variables
IE 360: Design and Control of
Industrial Systems I
Reference
Montgomery and Runger
Sections 4-1, 4-2, 4-3
Recall the difference between
continuous and discrete RVs
Let D be the diameter of a hole drill
Lecture 12
More Specific
Discrete Random Variables
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
3-7, 3-8, 3-9
Copyright 2010 by
Geometric RV
To be more concrete, think of flipping a
coin that has 30% chance of being
Lecture 11
Some Specific
Discrete Random Variables
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Sections 3-5, 3-6
Copyright 2010 by
Why look at some specific discrete
rvs?
Weve already spent a lot of time talking abo
Lecture 10
Joint Random Variables Part 2
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Section 5-2
Copyright 2010 by Joel Greenstein
Expected Value of Joint RVs
The expected value of joint rvs follows the same ideas a
Lecture 9
Introduction to Joint Random Variables
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Section 5-1
Copyright 2010 by Joel Greenstein
Overview of Joint RVs
We may want to consider more than one random
variable
Lecture 8
Mean and Variance of
Continuous Random Variables
IE 360: Design and Control of
Industrial Systems I
Reference
Montgomery and Runger
Section 4-4
Defining the Expected Value
The expected value (or mean or expectation) of a
continuous random variab
Lecture 6
Mean and Variance of
Discrete Random Variables
IE 360: Design and Control of
Industrial Systems I
Reference
Montgomery and Runger
Section 3-4
Some Introduction
Students always ask about the average and standard
deviation on tests. How come?
Beca
Lecture 5
Introduction to
Discrete Random Variables
IE 360: Design and Control of
Industrial Systems I
Reference
Montgomery and Runger
Sections 2-8, 3-1, 3-2, 33
What is a Random Variable
You mostly know what a random variable is already, we just need to
Lecture 4
Bayes Rule
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Section 2-7
Motivating the Law of Total
Probabilitysome number of
Imagine that a sample space is divided into
mutually exclusive events, and that thei
Lecture 3
Conditional Probability and
Multiplicative Rules
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Section 2-4, 2-5, 2-6
Review of Additive Rule
Blood Typing reflects the presence or absence of certain factors i
Lecture 2
Sample Spaces,
Events and Counting
IE 360: Design and Control of
Industrial Systems I
References
Montgomery and Runger
Sections 2-2, 2-3
Probability of an Event
To every point in the sample space, we
assign a weight or probability that the point
Lecture 1
Sample Spaces,
Events and Counting
IE 360: Design and Control of
Industrial Systems I
Reference
Montgomery and Runger
Section 2-1
Welcome to the world of chance
The real world is not deterministic
Every time a repeatable event happens, a
slightl
2-7 BAYES' THEOREM
phrase s. A specific design is randomly generated by the Web
server when you visit the site. Let A d enote the event that the
design color is red and Let B d enote the event that the font size
is not the smallest one . Are A a nd B i nd
50
CHAPTER 2 PROBABILITY
had a success rate o f 83% (289/350). This newer method
looked better, but the results changed when stone diameter
was considered. For stones with diameters less than two centimeters, 93% (81 /87) o f cases o f open surgery were s
2-5 MULTIPLICATION A ND T OTAL PROBABILITY RULES
2-5
47
\ .(ULTIPLICATION A ND T OTAL P ROBABILITY R ULES
The probability o f the intersection o f two events is often needed. The conditional probability
definition in Equation 2-9 can be rewritten to provi
H
com and canola. The following table shows the number o f
bottles o f these oils at a supermarket:
type o f oil
c om
canola
type o f
mono
unsaturation
poly
7
13
93
77
(a) If a bottle o f oil is selected at random, what is the probability that it belongs
2-3 ADDITION RULES
2 -71. A Web ad can be designed from four different colors,
three font types, five font sizes, three images, and five text
phrases. A specific design is randomly generated by the Web
server when you visit the site. I f you visit the sit
Erik lsakson/Getty Images, Inc.
Probability
A n athletic woman in her twenties arrives at the emergency department complaining o f
dizziness after running in hot weather. An electrocardiogram is used to check for a heart attack and the patient generates a
,. ~
Steve Shepard/iStockphoto
T he Role o f Statistics
i n Engineering
Statistics is a science that helps us make decisions and draw conclusions in the presence o f variability. For example, civil engineers working in the transportation field are
concer
Lecture 5 HW
Q2: True or False: The probability mass function for the number of jazz CDs when 4 CDs are selected at
random from a collection of 5 jazz CDs, 2 classical CDs and 3 rock CDs is
5 5
x 4 x , x = 0, 1, 2, 3, 4
f ( x) =
10
4
Solution:
First
Department of Industrial Engineering
IE 360 Design and Control of Industrial Systems I 3(3,0)
Summer Session I 2013
Instructor: Dr. Joel S. Greenstein
Office: 104B Freeman Hall
Office phone: 864-656-5649
E-mail address: [email protected]
Note: E-mail is t
Useful Results from the Lecture 12 PowerPoints that Are Not Covered in the Textbook
From slide 7 of the lecture notes:
The forgetfulness property of the geometric random variable:
P( X s | X = P( X (s t +1), s > t
t)
Useful Results from the Lecture 11 PowerPoints that Are Not Covered in the Textbook
From slide 4 of the lecture:
The expected value and variance of a discrete uniform random variable are given by:
k
k
Var[ X ] 1 ( xi x )2
x =
= E[ X ] 1 xi
=
ki
ki
= 1= 1
Useful Results from the Lecture 8 PowerPoints that Are Not Covered in the Textbook
Let X and Y be two random variables and c be a real number.
Rules of Expected Value (the same as for discrete random variables)
1. E[c] = c
2. E[cX ] = cE[ X ]
3. E[ X + Y=
Some Useful Results from the Lecture 7 PowerPoints that Are Not in the Textbook
For a continuous random variable X with cumulative distribution function F ( x) P( X x) :
P(a X b) P( X b) P( X a) F (b) F (a)
P( X a) 1 P( X a) 1 F (a)