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

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

3

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

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QLF (4) Variations

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nominal-the-best larger-the-best

smaller-the-best asymmetric

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

MSD: nominal-the-best

21

221

2

20

02

1

)(

)(

my

myn

MSDMSDk

Akmyk

yL n

ii

MSD: smaller-the-best

22

221

2

20

02

1

)(

)(

y

yn

MSDMSDk

Akyk

yL n

ii

MSD: larger-the-best

23

222

21

12

2002

111

11

)(

)(

n

n

i i

yyy

ynMSD

MSDk

yAky

k

yL

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)

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

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

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

The clearance between the cylinder and the piston of a six

cylinder engine be 3 (-2)(+7).

Solution: nominal-the-best

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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

Loss Function

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y-m

L(y)

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

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

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

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

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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