Brion Hurley Lean Six Sigma Black Belt Rockwell Collins

© 2015 Rockwell Collins. All rights reserved. Agenda Company Info Capability review Calculating yields from capability Calculating rolled yields Correlation review Predicting overall yields What to improve Questions 2

© 2015 Rockwell Collins. All rights reserved. 3 Rockwell Collins A global company operating from more than 60 locations in 27 countries 19,000 employees on our team Provides navigation, communications and display products and systems for military and commercial customers

© 2015 Rockwell Collins. All rights reserved. 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 4

© 2015 Rockwell Collins. All rights reserved. 1σ1σ Sigma Level vs Capability 5 6σ6σ LSLUSL Ppk = 2.0 4σ4σ Ppk = 1.33 Ppk = σ3σ Ppk = 1.0 GREAT! GOOD OK POOR CAPABILITY CONCLUSION SIGMA LEVEL

© 2015 Rockwell Collins. All rights reserved. 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 6 Std Dev WithinStd Dev Overall

© 2015 Rockwell Collins. All rights reserved. Good 7 Lots of margin between data and nearest limit Ppk = 2.18 Failure Rate = 0%

© 2015 Rockwell Collins. All rights reserved. Marginal 8 No margin between data and nearest limits Ppk = 0.76 Failure Rate = 2.2%

© 2015 Rockwell Collins. All rights reserved. Bad 9 Variation exceeds nearest limit Ppk = 0.08 Failure Rate = 40%

© 2015 Rockwell Collins. All rights reserved. What is acceptable? 10 LSL USL Cpk/Ppk < 1.0 Almost certain to see failures from normal process 1.0 < Cpk/Ppk < 1.67 Any slight shift in process may lead to failures 1.67 < Cpk/Ppk < 6.0 Very rare to see failures from normal process Cpk/Ppk > 6.0 Very rare to see failures from normal process that the measurement may no longer be necessary, or could be sampled

© 2015 Rockwell Collins. All rights reserved. Example 11 5 outliers out of 112 = 4.5%

© 2015 Rockwell Collins. All rights reserved. Removed Outliers 12 Ppk = 0.64 Failure Rate = 2.67%

© 2015 Rockwell Collins. All rights reserved. Rockwell Collins Proprietary Information 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% 13

© 2015 Rockwell Collins. All rights reserved. Rolled Test Yields 14 Probability of Passing All Tests = Product of Yields = * * * … * * = 15.4%

© 2015 Rockwell Collins. All rights reserved. What is correlation? 15

© 2015 Rockwell Collins. All rights reserved. No correlation 16

© 2015 Rockwell Collins. All rights reserved. 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 17

© 2015 Rockwell Collins. All rights reserved. Correlated Test Steps 18

© 2015 Rockwell Collins. All rights reserved. Adjusted Rolled Yield Calculation 19 Probability of Passing All Tests = Product of Yields = * * * … * * = 26.6%

© 2015 Rockwell Collins. All rights reserved. What to Improve? 20 Reduce Variation Eliminate Errors

© 2015 Rockwell Collins. All rights reserved. Non-normal distributions 21 Not a good fit to Normal distribution 0.6% failure rate Better fit to Lognormal distribution 4.6% failure rate

© 2015 Rockwell Collins. All rights reserved. © 2015 Rockwell Collins. All rights reserved. Brion Hurley Rockwell Collins Principal Lean Consultant Wilsonville, Oregon (Portland) For more information, visit

© 2015 Rockwell Collins. All rights reserved. Presentation Feedback 23 Thank you for attending! Your feedback is very important. Scanning this QR code will take you directly to the evaluation for this course.