Objective Functions in Robust Design

Pertemuan ke - 53 Oktober 2013

Today’s outline

� Review – Selection of Quality Characteristics

� Signal to noise ratios for static problemsproblems

� Application of signal to noise ratio –smaller the better

� Fraction defective analysis

Selection of Quality Selection of Quality

CharacteristicsCharacteristics

� Primary objective of robust design � select efficiency , robust condition which are reproducible in manufacturing condition

Selection of Quality Characteristics is prerequisite � Selection of Quality Characteristics is prerequisite for efficient, reliable and reproducible of experiment

� Selection of Quality Characteristics � important stage in DOE

Guidelines of Selection of Quality Guidelines of Selection of Quality

CharacteristicsCharacteristics

� Ideal function

� Continuous variable

Monotonic functions� Monotonic functions

� Ease to measurement

� Complete quality characteristics

� Modularization

Some considerations of Quality Some considerations of Quality

CharacteristicsCharacteristics

�Feeling of patient

�Percentage yield

�Difference

�Operating window

�Non-negative nominal the best

SN ratio for static problems

DOE can be classified1. Static functions

• Fixed target ( specific value )• Fixed target ( specific value )

2. Dynamic functions• Variable target

Noise Factors ( X )

Factors affecting a response

Y =f ( X , M , Z , R )

Y =f ( X , M , Z , R )

Response ( Y )Signal Factors ( M )

ControlFactors ( Z )

ScalingFactors ( R )

Signal factor

� Signal factor in TV sony system ( static system ) � constant � evaluate control and noise factor

� Signal factor in car breaking system ( dynamic system ) � The harder driver presses on the brake pedal

Importance of the SN ratio

� The objective of robust design �minimize the sensitivity of a quality characteristic to noise factors �characteristic to noise factors �based on mean square deviation

( )22 myMSD −+= σ

Importance of the SN ratio

� y = f ( X , M , Z , R )� In reality � function consisting

� predictable and unpredictable part � predictable and unpredictable part

� y = g( M , Z , R ) + e ( X , M , Z , R )� The objective of robust design �max

predictable and min unpredictable part

Importance of the SN ratio

� From experiment � variance of the predictable part (Vg) and variance of the unpredictable part (Ve) of the unpredictable part (Ve)

� Taguchi quality evaluation

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Importance of the SN ratio

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SN-ratio

� Smaller the better� Nominal the best� Larger the better� Larger the better� Signed target� Fraction defective� Operating window

SN-ratio - Nominal the best

=

2

2

10log10σµη

Two step optimization process

Relationship between SN ratio

and quality loss

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Example : Application SN ratio –

smaller the better

� Experiment to reduce the flash thickness in molded component

� Suppose � Seven 2-level factors ( A , B , C , D , E , F and G ) and three 2-level , C , D , E , F and G ) and three 2-level factors ( H, I and J )

� OA L8(27) � inner array � control factors and L4(23) � outer array � noise factor

Rata Variansi

SN ratio �first experiment

� Example� ExampleA �level 1 = ( -6.95 – 5.88 – 6.98 – 5.70 )/4 = -6.38level 2 = ( -9.62 – 9.36 – 10.64 – 5.58 )/4 = -8.80Diff = | -6.38 – (-8.80)| = 2.42

Application SN ratio – smaller

the better ( Conclusion )

� Significant factors � A , D and F� Saving 36 % of the original loss-to-

societysociety

Fraction defective analysis

� Example � wave soldering process� Holes in a printed circuit board get

blocked by solder bridging. It is a defect blocked by solder bridging. It is a defect since components cannot be inserted in these bridging holes.

Factors and level

Results

Response table

wave soldering process

conclusion

� Significant factors � D , F and B� Percent defective � 41 %

Diskusi