prof. dr. eng. ahmed sherif el-gizawy loss function -prof_el-gezawy.pdf · prof. dr. eng. ahmed...
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March 28, 2016
Prof. Dr. Eng. Ahmed Sherif El-GizawyDistinguished Adjunct Professor,
King Abdulaziz University, Saudi Arabia
Professor and Director Tech Development Center
University of Missouri, USA
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Presentation Style
interactive
participant-centered
realistic case studies
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Content Quality by Design (QBD)
Quality Loss functions (QLF)
Target Values for best performance
“Acceptable” versus Ideal Performance
Quadratic Loss Function
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Quality by Design QBD is one of the most powerful quality
improvement tools
QBD aims at development of high performance,
highly reliable services, products and processes that
are robust
It is important to quantify quality loss associated with
different services, product and process designs
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Quality Engineering Principles
Product
Life Cycle Costs
Manufacturing(fabrication)
Services(repairs &
replacements)
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Quality Engineering Principles
Q.E. concerns with reducing both these costs.
It is important to quantify quality loss associated with
different product and process designs.
The old method of measuring quality by fraction
defective (GO/NOGO method) is misleading.
Products with specification on the target values give
best performance.
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Example: TV Set Color Density
Sony Japan
Sony USA
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Recent Techniques in Q.E.
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P-Diagram A block diagram representation of the parameters
that influence the quality characteristics (responses,
performance and outputs) of the system
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P-Diagram Noise Factors
uncontrolled factors that cause Quality characteristics to deviate from their target value.
Types of Noise Factors1. Outer Noise: Variation in operating environment
2. Inner Noise: Deterioration of parts, variation on material properties
3. Between Product Noise: Variation between different machines or shifts
Robustness Product and process designs that are insensitive to noise factors
are Robust.
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Quality Loss
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Design Process
• prototype, materials, parts, components and assembly system
system
design
• set levels (values) of controllable factors to minimize the effect of noise factors
parameter
design
• determine the allowable variation of the controlled parameters without changing the quality
tolerance
design
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Design Process
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Robust Design Fundamentals Noise Factors
They are the uncontrolled factors that cause Quality characteristics to deviate from their target value
Robustness
System designs that are insensitive to noise factors are Robust
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Robust Systems Design
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Quality Loss Functions
Step Loss Function Quadratic Loss Function
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Quality Loss Function (QLF) loss is proportional to the square of deviation from
target value:
20
0
2)(
Ak
mykyL
valuetarget fromdeviation :
Constant:
at Loss Quality:
e)(Allaowanc Tolerance:
000
0
my
k
myA
17
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QLF (4) Variations
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nominal-the-best larger-the-best
smaller-the-best asymmetric
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QLF: Example The nominal value (target) of a TV set power supply is
m = 115 volts. When the voltage exceeds the range:
115 ± 20 volts
the average cost of repairing is $100
1) Evaluate the quality loss function
2) Assume that some adjustments have been made which
resulted in producing circuits with output = 110 volts,
evaluate the quality of the production
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QLF: Example
20
2
220
0
2
0
0
11525.0)(
25.020
100
20
100$
yyL
Ak
mykL
V
A
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MSD: nominal-the-best
21
221
2
20
02
1
)(
)(
my
myn
MSDMSDk
Akmyk
yL n
ii
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MSD: smaller-the-best
22
221
2
20
02
1
)(
)(
y
yn
MSDMSDk
Akyk
yL n
ii
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MSD: larger-the-best
23
222
21
12
2002
111
11
)(
)(
n
n
i i
yyy
ynMSD
MSDk
yAky
k
yL
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Example: smaller-the-best The quality characteristic of concern in injection molding
of a circuit breaker base is:
y : % shrinkage of the plastic base(y ≥ 0)
When the shrinkage is 1.5% or more, the product has to be replaced at a cost of $80.
Two different plastics were tested. The following table shows the % shrinkage values of the castings. Assuming the same cost in both cases, evaluate the results and make recommendations.
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Material
A 0.28 0.24 0.33 0.30 0.18 0.26 0.24 0.33
B 0.08 0.12 0.07 0.03 0.09 0.06 0.05 0.03
Data (% shrinkage)
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Example Answer
25
26.35)(
6.35
yyL
k
Material m
A 0.28 0.24 0.33 0.30 0.18 0.26 0.24 0.33 0.270 0.051
B 0.08 0.12 0.07 0.03 0.09 0.06 0.05 0.03 0.066 0.031
Data (% shrinkage)
221
2
20
02
1
)(
)(
y
yn
MSDMSDk
Akyk
yL n
ii
247.1
405.4
0351.0)(
1239.0)(
B
A
L
L
BMSD
AMSD
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Conclusion
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A B
L=4.4050 L=1.2468
The losses due to shrinkage in material A is
higher than in material B
So material B is better
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Case Study I An automobile manufacturer requires that the clearance
between the cylinder and the piston of a six cylinder engine be 3 (-2)(+7).
Defect loss for each cylinder and piston assembly is $200, and the monthly production is 50000 units.
Data showing deviation from the target value for the first two months of production are shown below. What are the quality levels during these two months?
What is the improvement, if any of the quality level?
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Month Deviations
1-2 3 0 4 5 -2 3 -2 0 -1 -1 -3
0 4 3 -2 0 1 0 5 6 2 -1
23 2 0 1 -1 -1 0 -2 3 0 2 4
6 -2 4 3 0 -2 0 -1
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The clearance between the cylinder and the piston of a six
cylinder engine be 3 (-2)(+7).
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Solution: nominal-the-best
29
22
308.4)(
08.47
200
yyL
k
221
2
20
02
1
)(
)(
my
myn
MSDMSDk
Akmyk
yL n
ii
butunsymmetrical
0myfor
22
350)(
502
200
yyL
k
0myfor
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Loss Function
30
y-m
L(y)
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Conclusion
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Month 1 Month 2• Total loss per unit 215.8
• Total loss $10,790,816
• Total loss per unit 155.3
• Total loss $ 7,766,035
There is an improvement in the process during month 2
since the total loss of quality is decreased
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Case Study II The strength of an adhesive is usually determined by the
kilograms force (kgf) needed to break apart specimens joined by the adhesive.
Two types of adhesives, S1 and S2, which cost $50 and $60 per unit weight, respectively, are to be compared.
The lower specification limits is 5 kgf for the breaking force. The out-of-specification units are discarded, resulting in a loss of $70 per unit. The annual production rate is 120,000 units.
Sixteen units were tested for each type of adhesive, and the following data for the breaking force were obtained:
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Adhesive Breaking force (kgf)
𝐒𝟏10.2 5.8 4.9 16.1 15.0 9.4 4.8 10.1
14.6 19.7 5.0 4.7 16.8 4.5 4.0 16.5
𝐒𝟐7.6 13.7 7.0 12.8 11.8 13.7 14.8 10.4
7.0 10.1 6.8 10.0 8.6 11.2 8.3 10.6
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Solution: larger-the-best
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2
2
8.2)(
8.25
70
yyL
k
222
21
12
2002
111
11
)(
)(
n
n
i i
yyy
ynMSD
MSDk
yAky
k
yL
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Conclusion
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S1 S2• Loss per unit $ 0.064
• Manufacture Cost $ 7,674
• Material Cost $50
• Total Loss $7,724
• Loss per unit $ 0.032
• Manufacture Cost $ 3,827
• Material Cost $60
• Total Loss $3,887
Even thought S1 is cheaper than S2, but the total loss of
quality is higher than S2
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This Presentation.. Quality by Design (QBD) is one of the most powerful quality improvement
tools.
QBD aims at development of high performance, highly reliable services, products and processes that are robust.
It is important to quantify quality loss associated with different services, product and process designs.
Products or services with specification on the target values give best performance.
Sole reliance on specification limits leads to a focus on “acceptable” performance rather than “ideal” performance.
The focus in the present seminar is on the application of the quadratic loss function to quantify improvement opportunities in engineering industry.
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Questions and Discussions..
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