Transcript Slide 1

Quality Control
Agenda
- What is quality?
- Approaches in quality control
- Accept/Reject testing
- Sampling (statistical QC)
- Control Charts
- Robust design methods
What is ‘Quality’
Performance:
- A product that ‘performs better’ than others at same function
Example:
Sound quality of Apple iPod vs. iRiver…
- Number of features, user interface
Examples:
Tri-Band mobile phone vs. Dual-Band mobile phone
Notebook cursor control (IBM joystick vs. touchpad)
What is ‘Quality’
Reliability:
- A product that needs frequent repair has ‘poor quality’
Example:
Consumer Reports surveyed the owners of > 1 million vehicles. To calculate
predicted reliability for 2006 model-year vehicles, the magazine averaged
overall reliability scores for the last three model years (two years for newer
models)
Best predicted reliability: Sporty cars/Convertibles Coupes
Honda S2000
Mazda MX-5 Miata (2005)
Lexus SC430
Chevrolet Monte Carlo (2005)
What is ‘Quality’
Durability:
- A product that has longer expected service life
Adidas Barricade 3 Men's Shoe
(6-Month outsole warranty)
Nike Air Resolve Plus Mid Men’s Shoe
(no warranty)
What is ‘Quality’
Aesthetics:
- A product that is ‘better looking’ or ‘more appealing’
Examples?
or
?
Defining quality for producers..
Example: [Montgomery]
- Real case study performed in ~1980 for a US car manufacturer
- Two suppliers of transmissions (gear-box) for same car model
Supplier 1: Japanese; Supplier 2: USA
- USA transmissions has 4x service/repair costs than Japan transmissions
Japan
Lower variability 
Lower failure rate
US
LSL
Target
USL
Distribution of critical dimensions from transmissions
Definitions
Quality is inversely proportional to variability
Quality improvement is the reduction in variability
of products/services.
How to reduce in variability of products/services ?
QC Approaches
(1) Accept/Reject testing
(2) Sampling (statistical QC)
(3) Statistical Process Control [Shewhart]
(4) Robust design methods (Design Of Experiments) [Taguchi]
Accept/Reject testing
- Find the ‘characteristic’ that defines quality
- Find a reliable, accurate method to measure it
- Measure each item
- All items outside the acceptance limits are scrapped
Lower Specified Limit
Upper Specified Limit
target
Measured characteristic
Problem with Accept/Reject testing
(1) May not be possible to measure all data
Examples:
Performance of Air-conditioning system, measure temperature of room
Pressure in soda can at 10°
(2) May be too expensive to measure each sample
Examples:
Service time for customers at McDonalds
Defective surface on small metal screw-heads
Problems with Accept/Reject testing
Solution: only measure a subset of all samples
This approach is called: Statistical Quality Control
What is statistics?
Background: Statistics
Average value (mean) and spread (standard deviation)
Given a list of n numbers, e.g.: 19, 21, 18, 20, 20, 21, 20, 20.
Mean = m = S ai / n = (19+21+18+20+20+21+20+20) / 8 = 19.875
The variance s2 =
2
(
a


)
 i
n
The standard deviation = s =
≈ 0.8594
2
(
a


)
 i
n
= √( s2) ≈ 0.927.
Background: Statistics..
Example. Air-conditioning system cools the living room and bedroom to 20;
Suppose now I want to know the average temperature in a room:
- Measure the temperature at 5 different locations in each room.
Living Room: 18, 19, 20, 21, 22.
Bedroom: 19, 20, 20, 20, 19.
What is the average temperature in the living room?
m = S ai / n = (18+19+20+21+22) / 5 = 20.
BUT: is m =  ?
Background: Statistics...
Example (continued) m = S ai / n = (18+19+20+21+22) / 5 = 20.
BUT: is m =  ?
If: sample points are selected randomly,
thermometer is accurate, …
then m is an unbiased estimator of .
- take many samples of 5 data points,
- the mean of the set of m-values will approach 
- how good is the estimate?
Background: Statistics....
Example. Air-conditioning system cools the living room and bedroom to 20;
Suppose now I want to know the variation of temperature in a room:
- Measure the temperature at 5 different locations in each room.
Living Room: 18, 19, 20, 21, 22.
sn =
BUT: is sn = s ?
 (a
i
 m) 2
n
≈ 1.4142
No!
The unbiased estimator of stdev of a sample = s =
2
(
a

m
)
 i
n 1
Sampling: Example
Soda can production:
Design spec: pressure of a sealed can 50PSI at 10C
Testing: sample few randomly selected cans each hour
Questions:
How many should we test?
Which cans should we select?
To Answer:
We need to know the distribution of pressure among all cans
Problem:
How can we know the distribution of pressure among all cans?
Sampling: Example..
How can we know the distribution of pressure among all cans?
%. of cans
Plot a histogram showing %-cans with pressure in different ranges
30
35
40
45
50
55
pressure (psi)
60
65
70
Sampling: Example…
Limit (as histogram step-size)  0: probability density function
1
s 2
30
35
40
45
55
50
pressure (psi)
60
65

e
( z   )2
2s 2
70
pdf is (almost) the familiar bell-shaped Gaussian curve!
why?
True Gaussian curve: [-∞ , ∞]; pressure: [0, 95psi]
Why is everything normal?
pdf of many natural random variables ~ normal distribution
WHY ?
Central Limit Theorem
Let X random variable, any pdf, mean, , and variance, s2
Let Sn = sum of n randomly selected values of X;
As n  ∞
Sn approaches normal distribution
with mean = nSn, and variance = ns2.
Central limit theorem..
X1 =
-1, with probability 1/3
0, with probability 1/3
1, with probability 1/3
p(S1)
Example
S1
X1 + X2
-1
-1
-1
0
0
0
1
1
1
-1
0
1
-1
0
1
-1
0
1
-2
-1
0
-1
0
1
0
1
2
X1 + X2 + X3 =
-3,
-2,
-1,
0,
1,
2,
3,
X1 + X2 =
with probability 1/27
with probability 3/27
with probability 6/27
with probability 7/27
with probability 6/27
with probability 3/27
with probability 1/27
-2,
-1,
0,
1,
2,
with probability 1/9
with probability 2/9
with probability 3/9
with probability 2/9
with probability 1/9
p(S2)
X2
S2
-2
1
0
-1
2
Gaussian curve
Curve joining p(S3)
p(S3)
X1
1
0
-1
S3
-3
-2
-1
0
1
2
3
(Weaker) Central Limit Theorem...
Let Sn = X1 + X2 + … + Xn
Different pdf, same  and s
normalized Sn is ~ normally distributed
Another Weak CLT:
Under some constraints, even if Xi are from different pdf’s,
with different  and s, the normalized sum is nearly normal!
Central Limit Therem....
Observation: For many physical processes/objects
variation is f( many independent factors)
effect of each individual factor is relatively small
Observation + CLT 
The variation of parameter(s) measuring the
physical phenomenon will follow Gaussian pdf
Sampling for QC
Soda Can Problem, recalled:
How can we know the distribution of pressure among all cans?
Answer:
We can assume it is normally distributed
Problem:
But what is the , s ?
Answer:
We will estimate these values
Outline