Chase Cats1d

8/9/2019 Chase Cats1d

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Complex Assemblies


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Process Variation

Standard Deviation

Rejects

Capability3

3 +3ULLL

+11

Mean

A frequency p lot shows ho w aprocess var ies from the mean


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Models for PredictingAssembly Tolerance Stackup

Worst Case (WC)

Statistical (RSS)

Six Sigma (6 )

Measured Data (Meas)

TASM = Ti

ASM =T

i3

2

ASM = Ti3C PK

2

ASM = i2


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Models for PredictingAssembly Tolerance Stackup

Model Stack Formula Predicts ApplicationWorstCase (WC)

TASM = Ti Extreme limits ofvariation.Not statistical.

Critical systems.No rejects p ermitted.Most costly.

Statistical(RSS) ASM = Ti3

2

Probable variation.Percent rejects

Reasonable e stimate.Some rejects al lowed.Less c ostly.

Six Sigma(6s) ASM

T i3C PK

2

Percent rejects.Drift in mean over timeis expected. Highquality levels d esired.

MeasuredData(Meas)

ASM = i2 Variation usingexisting parts.Percent rejects.After parts a re made.What-if? studies.


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Centering the Mean

Center

ULLL

Centering the process i n the LL/ULwindow minimizes rejects

Rejects

Xmean


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Higher Values MeanHigher Quality

6 5 4 3 2 1 0 +1 +2 +3 +4 +5 +6

4.5

3

6

ULLL


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Controlling Variation Leads toHigher Yields a nd Fewer Defects

Limits Yield Defects

3 99.73% 2700 / Million

4.5 99.99966% 3.4 / Million

6 99.9999998% 2 / Billion


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Controlling Variation Leads toHigher Yields a nd Fewer Defects

Limits Yield Defects

3 99.73% 2700 / Million

4.5 99.99966% 3.4 / Million

6 99.9999998% 2 / Billion


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Mean Shifts Happen

Mean variation is t ime-dependentdue t o tool wear, temperature, etc.

Mean Shift


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Accounting for Mean Shifts

1.5

The Six Sigma Model allows the en gineer to modelassembly variation due to mean shifts

4.5

ULLL


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Measures o f Process C apability

3

6

k

Process Capability Index:

Cp adjusted for k :

Cpk = C p (1-k)

CP =UL LL

6

UL

UL

LL

LL


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6 Variation Dened

RSS :

6 :

where C pk = C p (1-k)

and

ASM =Ti

3

2

ASM = Ti3C PK

2

CP =UL LL

6

3

ULLL

6

k

ULLL


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Requirements for High Quality

99.9999998%(Short Term)

99.99932%(Long Term)

6 Capability6 +6

LL UL

A goal of 4.5 long term requiresa 6 p rocess i n the short term


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Excel Statistical Functions

NORMDIST(x,mean,stand_dev,T/Fag)=area under the Normal distrib at point x

NORMSDIST(z)

=area under the Standard Normal distribSTANDARDIZE(x,mean,stand_dev)=(x - mean)/stand_dev

NORMSINV(Probability)=z corresp to a given probability(for z


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Statistical Function Accuracy

Source Yield Fraction 3 6

15 Place Math Tables 0.998650101968370000 0.9999999990130000006th Order Polynomial Fit 0.998650187471804000 0.999999998751939000Excel 0.998650032776765000 0.999999999009878000

Source Re ect Fraction !1" # 3 6

15 Place Math Tables $ 0.001349898031629990 0.0000000009870000006th Order Polynomial Fit 0.001349812528196100 0.000000001248061000Excel 0.001349967223235000 0.000000000990122000

Yield(1- Rejects

Z

* the 6 va lue is f rom an alternate source, accurate to 12 places.


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CATS 1-D Spreadsheet


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CATS 1-D Inputs


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Mean and Variance Comparison


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Yield and Rejects

Calculated in units, %, or parts-per-million


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Z ( u nits)

Mean

X = 0

Standard Deviation

x = 1.0

Transformation

Z = x xx

Standard Normal Distribution

ZL ZU

Used to determine % rejects f rom standard tables.Does not show mean shift.Transformed data all looks alike.


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What can CATS 1-D users expect?

Probably wont see:An end to poverty and miseryAll men treating each other as brothersWorld peace

But, you might notice:An increased understanding of the role of statistics in designFewer problems o n the factory oor

Engineering and production talking to each other without shouting.

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