IOE 466
Summary of Prerequisites
in Chapters 3 & 4 (Lectures 2~4)
Instructor: Prof. Judy Jin
Dept. of Industrial and Operations Engineering
The University of Michigan
1
IOE466 F16_Jin, Ch3&Ch4
Ask yourself?
For quality control, what are initial investigat

IOE 466 HW4 Solutions
6.32(a), (b), and Question (c) (1 point)
Given =10, x =2.5 . Sample size n=2 .
From Appendix VI:
A n=2=2.121
D 2 n=2=3.686, D1 n=2=0,d 2 n=2=1.128
B 6 n=2=2.606, B5 n=2=0, c 4 n=2 =0.7979
6.32 (a) x chart:
CL x =10
UCLx
2.5
= 3 x =10

IOE 466 HW1 Solution
3.31 (2 points)
(a) Total probability: (
(b) With
)
(
)
(
)
,
(
)
(
)
(
)
Mean:
[ ]
Variance:
(
)
(
(c) Cumulative distribution function ( )
this question, but can be any real number.
( )
)
(
(
). Note that
)
takes on the values of 1

IOE 466 Homework 7
Due: Thursday March. 24 before Class
Problem 1: problem 9.4 in textbook (3 points)
Hint for (b): use MR chart to estimate sigma. Compare whether the estimated sigma is close to the
assumed sigma.
Problem 2: problem 9.27 in textbook (1 p

IOE 466 Homework 8
Due: Thursday March 31 before Class
Problem 1: problem 8.24 in textbook and part (c)
(c) If the process is centered, what are Cp and its 95% confidence interval?
Problem 2: problem 8.32 in textbook and part (c)
Note:
Write out all the f

IOE 466 Statistical Quality Control
Practice Exam I
(80 mins)
NOTES:
Only one page (two sides) formula sheet is allowed (any other references should
NOT be put on the table.)
A calculator is allowed, but other electronic devices such as laptop, ipad, ipho

IOE 466 Statistical Quality Control
Practice Exam I
(80 mins)
NOTES:
Only one page (two sides) formula sheet is allowed (any other references should
NOT be put on the table.)
A calculator is allowed, but other electronic devices such as laptop, ipad, ip

IOE 466 W16
Exam 1
(Feb 25, Thursday at
12:10~1:30, 80 mins)
Rules & Review
1
Exam Rules:
You must go to your assigned exam room. Please check
your exam room location before the exam
Last name A-Wa at Beyster 1670
Last name Wu-Z at EECS 3433
Except for ca

IOE 466
Summary of Prerequisites
in Chapters 3 & 4 (Lectures 2~4)
Instructor: Prof. Judy Jin
Dept. of Industrial and Operations Engineering
The University of Michigan
1
IOE466W16_Jin, Ch3&Ch4
Need for Statistics
Quality is evaluated by the variability, a

IOE 466 HW3 Solutions
5.2 (1 point)
The control chart is mathematically equivalent to a series of statistical hypothesis tests. If a plot
point is within control limits, say for the average X , the null hypothesis that the mean is
some value is not reject

IOE 466 Homework 6
Due: Thursday Nov. 3 before Class
Problem 1: (0.5 + 0.75 + 0.75 = 2 points)
(c) If the process is getting worse with the average 5 nonconformities per machine
(calculator), what is the probability of Type II error this control chart?
No

IOE 466-Statistical Quality Control
Ch9 CUSUM/ EWMA/ MA
(Lectures 14 -16)
Instructor: Judy Jin
Department of Industrial and Operations Engineering
The University of Michigan
IOE466F16, Jin, Ch9 CUSUM / EWMA / MA
1
Ask yourself?
What control charts have y

IOE 466 - Statistical Quality Control
Ch7: Control Charts for Attributes
(Lectures 10~13)
Instructor: Judy Jin
Professor
Department of Industrial and Operations Engineering
The University of Michigan
IOE 466F16 Jin, Ch7_Control Charts for Attributes
1
Ask

Statistical Inference:
Inference for mean variance known:
Null hypothesis:
Alternativ
e
Hypothesi
s
H 0 : =0
Inference for mean variance unknown:
. Test statistic:
X 0
Z0=
n
Null hypothesis:
Alternative
Hypothesis
Rejection
Region
Confidence
Interval
H 1

IOE 466 Statistical Quality Control
Practice Exam II
NOTES:
Only two pages (two sides) formula sheet are allowed (any other references should NOT
be put on the table).
A calculator is allowed, but other electronic devices such as laptop, iPad, smartphon

IOE 466 Homework 9
Due: Tuesday Nov. 29 before Class
Problem 1) (3 points)
Use Excel to calculate the acceptance probability for a lot with fraction defective range as
(0.01, 0.06, 0.07, 0.08, 0.09) based on the rule of n = 100 and c = 3. Does this rule m

IOE 466 Homework 7
Due: Thursday Nov. 10 before Class
Problem 1: problem 9.4 in textbook (3 points)
Hint for (b): use MR chart to estimate sigma. Compare whether the estimated sigma is close to the
assumed sigma. (You do not need to do hypothesis testing)

Control Charts for Nonconformities:
Units
N1
Sample unit:
Inspection unit:
N2
n=N 1 /N 2
Sample size:
c-chart (Defects per sample)
UCL= c + L c
m
Di
CL=c = i=1
m
LCL=c L c
Type I and II Error for
c charts
=P ( D LCLD UCLH 0 )
=1P cfw_ LC Lc < D<UC Lc H

IOE 466 Homework 5
Problem 1: problem 7.34 in textbook (2 points)
Problem 2: problem 7.40 in textbook & part (c) (3 points)
(c) What is Type I error of this control chart?
Note: Please use the Binomial distribution for solving (b) and (c) rather than the

IOE 466 Homework 8
Due: Thursday Nov. 17 before Class
Problem 1: problem 8.24 in textbook and part (c) (0.5 + 0.5 +1 = 2 points)
(c) If the process mean can be centered to its design target, what are Cp and its 95%
confidence interval?
Hint: you can assum

IOE 466 - Statistical Quality Control
Ch6: Control Charts for Variables
Instructor: Judy Jin
Department of Industrial and Operations Engineering
The University of Michigan
jhjin@umich.edu
IOE466W16_Jin, Ch6_Control Charts for Variables
1
Ask Yourself
How

IOE 466 - Statistical Quality Control
Ch5: Methods and Philosophy of
Statistical Process Control
(Lectures 5 &6)
Instructor: Judy Jin
Professor
Department of Industrial and Operations Engineering
The University of Michigan
jhjin@umich.edu
IOE466W16_Jin, M

IOE 466 Homework 9
Due: Thursday April. 14 before Class
Problem 1:
Consider the partially filled ANOVA table below from a Gage R&R experiment. Within
each group, four products were measured by three operators with two replicates.
(a) Fill in the blanks in

IOE 466 Homework 3
Due: Thursday Feb. 4 before Class
Problem 1: problem 5.16 on page 231 in textbook (1 point)
Problem 2: problem 5.18 on page 231 in textbook (1 point)
Hint: the upper and lower control limits are computed based on the +3 and -3 limits
re

IOE 466-Statistical Quality Control
Ch9 CUSUM/ EWMA/ MA
(Lectures 14 -16)
Instructor: Judy Jin
Department of Industrial and Operations Engineering
The University of Michigan
IOE466W16, Jin, Ch9 CUSUM / EWMA / MA
1
Ask yourself?
What control charts have y

IOE 466 Homework 1
Due: Thursday Jan. 21 before Class
Problem 1: problem 1.3 on page 47 in textbook
Problem 2: problem 3.8 on page 103 in textbook
Note: You can use Excel, Minitab, etc. for this question.
IOE 466 Homework 1
Due: Thursday Jan. 21 before Cl

IOE 466 Homework 2
Due: Thursday Jan. 28 before Class
Problem 1: problem 4.4 (b) & (d) on page 175 in textbook
(hint: you can use Excel to get the P-values or use the t-table to get the
bounds)
Problem 2: problem 4.8 on page 176 in textbook
Page 1 of 3
IO

IOE 466 Homework 6
Due: Thursday March. 17 before Class
Problem 1: (2 points)
(c) If the process is getting worse with the average 5 nonconformities per machine,
what is the probability of Type II error this control chart ?
Note: you may assume that both

IOE 466 - Statistical Quality Control
Methods and Philosophy of
Statistical Process Control
(Lectures 5 &6)
Instructor: Judy Jin
Professor
Department of Industrial and Operations Engineering
The University of Michigan
jhjin@umich.edu
1
IOE466F16_Jin, Meth