1. TM 720: Statistical Process Control
IENG Lecture 04
Quality Matters:
Cost of Quality, Yield and Variance Reduction
1/17/2019
IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

2. Quality is a multifaceted entity.
TM 720: Statistical Process Control
Quality is a multifaceted entity.
Traditional (OLD) definition of Quality:
Fitness for Use (i.e., products must meet requirements of those who use them.)
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IENG 451 Operational Strategies
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3. Two Aspects of “Fitness for Use”
TM 720: Statistical Process Control
Two Aspects of “Fitness for Use”
Quality of Design –
all products intentionally made in various grades of quality. (e.g., Autos differ with respect to size, options, speed, etc.)
Quality of Conformance –
how well the product conforms to specifications. (e.g., If diameter of a drilled hole is within specifications then it has good quality.)
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IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

4. What's Wrong with "Fitness for Use" Definition of Quality?
TM 720: Statistical Process Control
What's Wrong with "Fitness for Use" Definition of Quality?
Unfortunately, quality as “Fitness for Use” has become associated with the "conformance to specifications" regardless of whether or not the product is fit for use by customer.
Common Misconception:
Quality can be dealt with solely in manufacturing - that is, by "gold plating" the product
1/17/2019
IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

5. Cost of Quality Myth: Higher Quality  Higher Cost
TM 720: Statistical Process Control
Cost of Quality Myth: Higher Quality  Higher Cost $
Defect Rate
Quality Cost
Total Cost
Failure
Cost
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IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

6. Reduction of Variability
TM 720: Statistical Process Control
Reduction of Variability
Modern Definition of Quality:
Quality is inversely proportional to variability
If variability of product decreases  quality of product increases
Quality Improvement –
Reduction of variability in processes and products
1/17/2019
IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

7. Cost of (Poor) Quality: Higher Quality  Lower Cost
TM 720: Statistical Process Control
Cost of (Poor) Quality: Higher Quality  Lower Cost
Example: Manufacture of Copier Part
Manufacturing Process
$20 / part
75% Conform
100 parts
(75 good parts)
25% Non-conforming:
(10 scrap parts)
(25 parts)
Re-work Process
$4 / part
(15 good parts)
1/17/2019
IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

8. Study finds excessive process variability causes high defect rate
TM 720: Statistical Process Control
Study finds excessive process variability causes high defect rate
New process implemented
NOW: manufacturing non-conformities = 5%
SAVINGS: $22.89 – $20.53 = $2.36 / good part
PRODUCTIVITY: 9% improvement
1/17/2019
IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

9. Understanding Process Variation
Three Aspects:
Location
Spread
Shape
Independence:
changing Location does not impact Spread
Frequently, the CLT lets us use Normal Curve
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IENG 451 Operational Strategies

10. IENG 451 Operational Strategies
Shape: Distributions
Distributions quantify the probability of an event
Events near the mean are most likely to occur, events further away are less likely to be observed
35.0  2.5
30.4
(-3)
34.8 (-)
39.2 (+)
43.6
(+3)
32.6
(-2) 37
()
41.4
(+2)
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11. Standard Normal Distribution
The Standard Normal Distribution has a mean () of 0 and a standard deviation () of 1
Total area under the curve, (z), from z = – to z =  is exactly 1 ( -or- 100% of the observations)
The curve is symmetric about the mean
Half of the total area lays on either side, so:
(– z) = 1 – (z)
(z) z 
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IENG 451 Operational Strategies

12. Standard Normal Distribution
How likely is it that we would observe a data point more than 2.57 standard deviations beyond the mean?
Area under the curve from – to z = 2.5  is found by using the Standard Normal table, looking up the cumulative area for z = 2.57, and then subtracting the cumulative area from 1.
(z) z 
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IENG 451 Operational Strategies

13. IENG 451 Operational Strategies
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IENG 451 Operational Strategies

14. Standard Normal Distribution
How likely is it that we would observe a data point more than 2.57 standard deviations beyond the mean?
Area under the curve from – to z = 2.5  is found by using the table on pp , looking up the cumulative area for z = 2.57, and then subtracting the cumulative area from 1.
Answer: 1 – = , or about 5 times in 1000
(z) z 
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15. What if the distribution isn’t a Standard Normal Distribution?
If it is from any Normal Distribution, we can express the difference from an observation to the mean in units of the standard deviation, and this converts it to a Standard Normal Distribution.
Conversion formula is:
where:
x is the point in the interval,
 is the population mean, and
 is the population standard deviation.
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16. Example: Process Yield
Specifications are often set irrespective of process distribution, but if we understand our process we can estimate yield / defects.
Assume a specification calls for a value of 35.0  2.5.
Assume the process has a distribution that is Normally distributed, with a mean of 37.0 and a standard deviation of 2.20.
Estimate the proportion of the process output that will meet specifications.
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17. TM 720: Statistical Process Control
Six Sigma - Motorola
Six Sigma* = 3.4 defects per million opportunities!
± 6 standard deviations – after a 1.5 sigma shift!
Every Motorola employee must show bottom line results of quality project – finance, mail room, manufacturing, etc.
identify problem;
develop measurement;
set goal;
close gap
Long term process – 5 years to fully implement
1/17/2019
IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl

18. TM 720: Statistical Process Control
Questions & Issues
There WILL be a lab tomorrow:
It is a follow-on from last week, covering process improvement
Variation effects
Cost of (poor) Quality
1/17/2019
IENG 451 Operational Strategies
(c) D.H. Jensen & R.C. Wurl