IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #2
1
Probability Distributions
A probability distribution is a mathematical model that
relates the value of the variable with the probability of
occurrence of that value in the population.
Two ty

99
E xercises
I.xercises
OJ
-:re Student
).=;.ucrce Manual
~ nts c ompre
:n=L"jve a nnotated
,.;lm:ions to the
tOO-numbered
~=cises i ncluded
] I : he A nswers to
Sc:.'ffted Exercises
ie.-rion i n the
na:t o f this book.
3.1. T he content o f liquid deter

IEE 474
Take Home Quiz
th
Due: Thursday, March 24 at 3:00 PM in class
Directions: Use either Minitab or JMP to complete the following problems. Provide images of
the control charts from the software in your solutions. Note: Both Minitab and JMP allow you

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #1
1
About me.
2
2000
Tsinghua University, China
B.S. Civil Engineering
3
2007
University of
Michigan, Ann
Arbor
M.A., Ph.D.
Industrial and
Operations
Engineering
4
Now
Industrial Engineering,

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #19
1
Ch15 Acceptance Sampling for Attributes
What is acceptance sampling?
Why use acceptance sampling?
Types of Sampling Plans
Single sampling plan
Double sampling plan
Multiple-sampling pla

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #18
1
Review - Statistical Quality Control Methods
Three major quality control methods: SPC, DOE (design
of experiments), and acceptance sampling.
A simple example to illustrate the three methods

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #17
1
Gage and Measurement System Capability
Why need it?
Total variability decomposition
Total
True value of Measurement
observed
error
measurement measurement
y =+
x
2
2
2
Total = P + Gauge
8-15

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes # 12
1
Chapter 9 - CUSUM & EWMA Control Charts
To expedite detection of a small mean shift in the process.
Shewhart chart
takes a long time to detect a small mean shift (shift<1.5 )
only uses the

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #13
1
Chapter 10
Other Univariate Statistical ProcessMonitoring and Control Techniques
SPC for Short Production Runs
SPC with Autocorrelated Process Data
2
10-1 SPC for Short Production Runs
I. Why

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #15
1
Chp 8 Process and Measurement System
Capability Analysis
1) Predicting ability to hold tolerances.
2) Assist product developers/designers in selecting
/designing processes.
3) Assist in estab

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #7
1
Ch 5. Methods and Philosophy of SPC
Chance Causes and Assignable Causes of
Variations
Statistical Basis of Control Charts
Implementation of SPC and Case Studies
2
Chance Cause & Assignable

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #6
1
Inference on the Variance of a Normal Distribution
( n 1) s 2
2
~ 2 ( n 1)
2
H 0 :
2
0
2
0
( n 1) s 2
2
0
2
2
2
If 0 / 2,n 1 or 0 12 / 2,n 1
2
2
0
2
2
0
If
2
02 ,n 1
2
H1 : 2 0
If
02 12 ,n

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #5
1
The Use of P-Values in Hypothesis Testing
1.
Traditional hypothesis testing:
Given to determine whether the null hypothesis was rejected
Disadvantage:
No information on how close to/far awa

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #11
1
Control Charts for Nonconformities (Defects)
- C and U Charts
Why need it? Control the number of nonconformities
A nonconforming product does not satisfy one or more of the
specifications

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #10
1
Ch7 Control Charts for Attributes
Nonconforming: Defective
Conforming: Non-defective
Attributes: Quality characteristics of conforming or non
conforming
The fraction nonconforming: the ra

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #8
1
Ch 6 Control Charts for Variables
Need for Control of Both Mean and Variability
The number of nonconforming products is dependent on both mean
shift and larger variation
Nominal mean and nom

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #9
1
Two Types of Variability
X-bar chart monitors process average, or between
sample variability; R chart monitors within sample
variability.
Estimate of process standard deviation reflects with

Midterm exam topics (from Teaching
Plan)
Instructions for midterm exam
A sheet with notes (both side) will be allowed for the exam
The exam will be closed notes, closed books. However, you
will be able (and need) to use the discount tables that
come at

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #1
1
Syllabus
Call for an appointment if office hours do not fit
your schedule.
2
Dimension of Quality
Reliability
Durability
Serviceability
Aesthetics
Ease of use
Reputation
3
Quality Definitions

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #2
1
Probability Distributions
A probability distribution is a mathematical model that
relates the value of the variable with the probability of
occurrence of that value in the population.
Two ty

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #2
1
Probability Distributions
A probability distribution is a mathematical model that
relates the value of the variable with the probability of
occurrence of that value in the population.
Two ty

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #3
1
Poisson Distribution
Poisson Distribution: the number of random events occurring during a
specific time period with the average occurrence rate known:
e x
p( x)
, x 0,1,.
x!
,
2
Examples:

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #4
1
Chapter 4 Inference About Process Quality
The need of Statistical Inference
In statistical quality control, the probability distribution is
used to model some quality characteristic.
The pa

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #14
1
Ch. 11 Multivariate Quality Control
Monitoring of Process Mean
Chi-square Control Chart
Hotelling T2 control chart
sample size n>1
Sample size n=1
Interpretation of out-of-control signal

IEE 474 Quality Control
Instructor: Jing Li
Lecture notes #16
1
Setting Specification Limits on
Discrete Components
To analyze final product capability based on
tolerance of each component
To determine specification limits on the
individual components s

IEE 474 HW6
Due: 11/3/2008
10-1
A 2.530, nA 15, A 101.40
B 2.297, nB 9, B 60.444
C 1.815, nC 18, C 75.333
D 1.875, nD 18, D 50.111
Standard deviations are approximately the same, so the DNOM chart can be used.
R 3.8, 2.245, n 3
x chart: CL = 0.55, UCL

IEE 474
HW7
Due: 11/10/2008
11-1
Phase 2 T 2 control charts with m = 50 preliminary samples, n = 25 sample size, p = 2
characteristics. Let = 0.001.
p (m + 1)(n 1)
F , p ,mn m p +1
mn m p + 1
2(50 + 1)(25 1)
=
F0.001,2,1199
50(25) 50 2 + 1
UCL =
= ( 2448