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 - Statistical Quality Control
Ch7: Control Charts for Attributes
March 8, 2016
1
IOE 466W16 Jin, Ch7_Control Charts for Attributes
Outline
Review c and u charts
Statistical assumptions
Monitoring unit vs. sampling unit
Control limits calculati

6-70 CHAPTER 6 CONTROL CHARTS FOR VARIABLES
6.58.
A normally distributed quality characteristic is monitored through use of an x and R chart. These charts have
the following parameters (n = 4):
Both charts exhibit control.
(a) What is the estimated standa

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-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 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 Homework 9
Due: Thursday Apr. 14 before Class
Problem 1: (5 points)
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

IOE 466 Homework 6
Due: Thursday March. 17 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,
what is the probability of Type II error this control chart ?
Note: you m

IOE 466 Statistical Quality Control
Exam I (Feb. 25, 2015)
12:00~1:30 pm (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 suc

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 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.
(a) K k 0.5 0.05 0.025; H h 4.77 0.05 0.

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-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-Statistical Quality Control
Lec 18-20
Ch8: Measurement System Analysis
Instructor: Judy Jin
Professor
Department of Industrial and Operations Engineering
The University of Michigan
IOE466_W16_Measurement System Analysis
1
Ask Yourself
What is gau

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)
(b) From Appendix IV (t table) and = 19,
0.05
0.025
1.729
1.8

Final Exam
Rules & Review
IOE 466 W16
1
When, Where
When: April 21 (TH) 4~6pm (SHARP)
Where: 1670 Beyster.
2
1
Information:
You are ONLY allowed to bring
A calculator.
Except for calculator, you cannot use any other electronic
device, such as Laptop, ipa

IOE 466
Statistical Quality Control
Lecture 17
Ch8: Process Capability Analysis
Instructor: Judy Jin
Professor
Department of Industrial and Operations Engineering
The University of Michigan
1
IOE 466_W16, Judy Jin
Process Capability Assessment
A processs

IOE 466 Homework 8
Due: Thursday March. 31 before Class
Problem 1: problem 8.24 in textbook and part (c) (1 + 2 +2 = 5 points)
(c) If the process mean can be centered to its design target, what are Cp and its 95%
confidence interval?
USL 100; LSL 90; n 30

IOE 466 Homework 1
Due: Thursday Jan. 21 before Class
Problem 1: problem 1.3 on page 47 in textbook (1 point)
Solution: there are many products that can be used for illustration, and here we take
the computers as an example.
(1) Performance. A computer sh

IOE 466 Homework 5
Problem 1: problem 7.34 in textbook (2 points)
Solution:
We need to find n such that Pr D 1 0.9 Pr D 0 1 0.9 0.1 .
From the binomial distribution,
n
n
n
Pr D 0 1 p 1 0.01 0.99n 0.1
0
n ln 0.99 ln 0.1
ln 0.1
229.1
ln 0.99
n 230
n
Ther

IOE 466 Homework 4
Due: Thursday Feb. 11 before Class
Problem 1: problem 6.32 in textbook, (a) & (b) only, (c) see below (1.5
points)
(c) What are the warning control limits using K = 2 for x-bar and R charts?
Solution:
= 2, = 10, = 2.5. These are standa

IOE 466 Homework 3 Solution
Problem 1: problem 5.16 on page 231 in textbook (1 point)
Solution:
Type I and II error probabilities contain information on statistical performance; an ARL
results from their selection. ARL is more meaningful since its nature