Brion Hurley Lean Six Sigma Black Belt Rockwell Collins.

Using Capability Analysis to Predict New Product YieldsBrion HurleyLean Six Sigma Black BeltRockwell Collins

© 2015 Rockwell Collins. All rights reserved.

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Agenda

• Company Info• Capability review• Calculating yields from capability• Calculating rolled yields• Correlation review• Predicting overall yields• What to improve• Questions


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Rockwell Collins

• A global company operating from more than 60 locationsin 27 countries

• 19,000 employees on our team

• Provides navigation, communications and display products and systems for military and commercial customers


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Capability Refresher

• How well does your variable (measurable) data fit within your specification limits?

• Ratio of process variation compared to specification range

– Want the specification range to be wider than process variation!

• The easier the process fits within limits, the more “capable” it is

• Calculated by Cpk and Ppk, where higher number is better


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1σ

Sigma Level vs Capability

6σ

LSL USL

Ppk = 2.0

4σPpk = 1.33

Ppk = 0.33

3σPpk = 1.0

GREAT!

GOOD

OK

POOR

CAPABILITY CONCLUSIONSIGMA LEVEL


Capability Indices (Cpk and Ppk)

• Cpk and Ppk are a better measure of how well the data fits within the specification limit(s), as it takes the average (location) of the data into account

• Can be calculated with one or two-sided limits

• Only difference is what to use for s• Cpk uses standard deviation within• Ppk uses standard deviation overall

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Std Dev Within

s

LSLxC pl 3

s

xUSLC pu 3

),min( puplpk CCC

s

LSLxPpl 3

s

xUSLPpu 3

),min( puplpk PPP

Std Dev Overall


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GoodLots of margin between data and nearest limit

Ppk = 2.18

Failure Rate = 0%


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MarginalNo margin between data and nearest limits

Ppk = 0.76

Failure Rate = 2.2%


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BadVariation exceeds nearest limit

Ppk = 0.08

Failure Rate = 40%


What is acceptable?

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LSL USL LSL USL LSL USL LSL USL

Cpk/Ppk < 1.0Almost certain to see failures from normal process

1.0 < Cpk/Ppk < 1.67Any slight shift in

process may lead to failures

1.67 < Cpk/Ppk < 6.0Very rare to see

failures from normal process

Cpk/Ppk > 6.0Very rare to see failures from

normal process that the measurement may no longer

be necessary, or could be sampled


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Example 5 outliers out of 112 = 4.5%


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Removed Outliers

Ppk = 0.64

Failure Rate = 2.67%


Rockwell Collins Proprietary Information 13

Calculating Yield for Test X

• Failures due to outliers– Observed 5 out of 112 = 4.5%

• Failures predicted from variation– Ppk = 0.64– Failure Rate = 2.67%

• Probability of Failing Test = 2.67% + 4.5% = 7.2%

• Probability of Passing Test = 100% - 7.2% = 92.8%


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Rolled Test Yields

Probability of Passing All Tests = Product of Yields= 0.969 * 0.846 * 0.913 * … * 0.883 * 0.873 = 15.4%

Test PpkPredicted Common

Cause Fallout OutliersPredicted

Failure RatePredicted

Yield1 1.2 0.2% 2.9% 3.1% 96.9%2 0.33 12.5% 2.9% 15.4% 84.6%

3A 0.37 8.7% 0.0% 8.7% 91.3%3B 0.34 12.3% 4.3% 16.6% 83.4%4 1.72 0.0% 4.3% 4.3% 95.7%5 1.58 0.0% 0.0% 0.0% 100.0%6 0.25 19.2% 0.0% 19.2% 80.8%7 0.23 23.8% 4.3% 28.1% 71.9%

8A 0.23 19.5% 0.0% 19.5% 80.5%8B 0.35 8.5% 0.0% 8.5% 91.5%9A 0.35 12.5% 0.0% 12.5% 87.5%9B 0.38 10.7% 0.0% 10.7% 89.3%9C 0.36 11.7% 0.0% 11.7% 88.3%9D 0.34 12.7% 0.0% 12.7% 87.3%


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What is correlation?


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No correlation


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Why is correlation important?

• If results are not correlated (correlation < 0.70), then failures or defects may show up randomly (independent)– All tests have own probability of failure

• If results are strongly correlated (correlation >= 0.70), then failures or defects may show up at the same time (dependent)– Only take worse case scenario of correlated tests


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Correlated Test Steps




Yield1 1.2 0.2% 2.9% 3.1% 96.9%2 0.33 12.5% 2.9% 15.4% 84.6%

3A 0.37 8.7% 0.0% 8.7% 91.3%3B 0.34 12.3% 4.3% 16.6% 83.4%4 1.72 0.0% 4.3% 4.3% 95.7%5 1.58 0.0% 0.0% 0.0% 100.0%6 0.25 19.2% 0.0% 19.2% 80.8%7 0.23 23.8% 4.3% 28.1% 71.9%

8A 0.23 19.5% 0.0% 19.5% 80.5%8B 0.35 8.5% 0.0% 8.5% 91.5%9A 0.35 12.5% 0.0% 12.5% 87.5%9B 0.38 10.7% 0.0% 10.7% 89.3%9C 0.36 11.7% 0.0% 11.7% 88.3%9D 0.34 12.7% 0.0% 12.7% 87.3%


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Adjusted Rolled Yield Calculation




YieldCorrelated

Yield1 1.2 0.2% 2.9% 3.1% 96.9% 96.9%2 0.33 12.5% 2.9% 15.4% 84.6% 84.6%

3A 0.37 8.7% 0.0% 8.7% 91.3%3B 0.34 12.3% 4.3% 16.6% 83.4%4 1.72 0.0% 4.3% 4.3% 95.7% 95.7%5 1.58 0.0% 0.0% 0.0% 100.0% 100.0%6 0.25 19.2% 0.0% 19.2% 80.8% 80.8%7 0.23 23.8% 4.3% 28.1% 71.9% 71.9%

8A 0.23 19.5% 0.0% 19.5% 80.5%8B 0.35 8.5% 0.0% 8.5% 91.5%9A 0.35 12.5% 0.0% 12.5% 87.5%9B 0.38 10.7% 0.0% 10.7% 89.3%9C 0.36 11.7% 0.0% 11.7% 88.3%9D 0.34 12.7% 0.0% 12.7% 87.3%

87.3%

83.4%

80.5%

Probability of Passing All Tests = Product of Yields= 0.969 * 0.846 * 0.913 * … * 0.883 * 0.873 = 26.6%


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What to Improve?




YieldCorrelated

Yield1 1.2 0.2% 2.9% 3.1% 96.9% 96.9%2 0.33 12.5% 2.9% 15.4% 84.6% 84.6%

3A 0.37 8.7% 0.0% 8.7% 91.3%3B 0.34 12.3% 4.3% 16.6% 83.4%4 1.72 0.0% 4.3% 4.3% 95.7% 95.7%5 1.58 0.0% 0.0% 0.0% 100.0% 100.0%6 0.25 19.2% 0.0% 19.2% 80.8% 80.8%7 0.23 23.8% 4.3% 28.1% 71.9% 71.9%

8A 0.23 19.5% 0.0% 19.5% 80.5%8B 0.35 8.5% 0.0% 8.5% 91.5%9A 0.35 12.5% 0.0% 12.5% 87.5%9B 0.38 10.7% 0.0% 10.7% 89.3%9C 0.36 11.7% 0.0% 11.7% 88.3%9D 0.34 12.7% 0.0% 12.7% 87.3%

87.3%

83.4%

80.5%

Reduce VariationEliminate Errors


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Non-normal distributions

Not a good fit toNormal distribution0.6% failure rate

Better fit toLognormal distribution

4.6% failure rate



Brion HurleyRockwell CollinsPrincipal Lean ConsultantWilsonville, Oregon (Portland)[email protected]

For more information, visit www.rockwellcollins.com

mailto:[email protected]


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