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©20
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Design for Six Sigma with MATLAB®
Kevin Cohan
The MathWorks, Inc.
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Design for Six Sigma
http://www.dtic.mil/ndia/2003test/kiemele.pdf
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Product StageResearch Design Development Production
“Classic” Six Sigmafocuses here
DFSS focuses here
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DMAIC Methodology
Define the problem / defects
Measure the current performance level
Analyze to determine the root causes of the problem / defects
Improve by identifying and implementing solutionsthat eliminate the root causes
Control by monitoring the performance of the improved process
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http://www.dtic.mil/ndia/2003test/kiemele.pdf
D M A I C
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Example
Optimization of anEngine Cooling Fan Design
Image courtesy of Novak Conversions
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Define:Define the Problem
Existing engine isn’t cooled sufficientlyunder difficult driving conditions
New design requirementAirflow > 875 cubic feet per minute
ApproachOptimize design factorsfor maximum airflowUse the MATLAB product family toimplement the DMAIC methodology
D M A I C
Image courtesy of Novak Conversions
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Measure:Measure Cooling Fan Performance
Import historical datafrom Excel
Establish baselinefor comparison
Mean = 842 ft3 / minStd Dev = + 2 ft3 / min
D M A I C
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Analyze:Analyze Factors that Affect Performance
Three design factorswe can modify
Clearance Distance
Pitch
Min MaxDistance from radiator (d) 1.0 1.5 inchesBlade pitch angle (p) 15 35 degreesBlade tip clearance (c) 1.0 2.0 inches
FactorsRange
Units
D M A I C
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Analyze:Analyze Factors that Affect Performance
Gather additional data from existing systemModify our design factors and measure performanceFit a model to the performance dataEvaluate the model to understand theeffect of each design factor
What tests do we run?… and how many?
D M A I C
(d)
(p)
(c)
Test Run Dis
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rad
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Bla
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Bla
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Perf
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1 ? ? ?23…n
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Analyze:Analyze Factors that Affect Performance
Use a designed experiment to gather performance dataChoose the Box-Behnken function to determinepoints in the design space
D M A I C
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Analyze:Analyze Factors that Affect Performance
Fit a quadratic model to the data (regstats function)
D M A I C
AF = B0 + B1X1 + B2X2 + B3X3 +B4X1X2 + B5X1X3 + B6X2X3 +B7X12 + B8X22 + B9X32
AF = Airflow (ft3/min)X1 = Distance from radiator (inches)X2 = Fan pitch angle (degrees)X3 = Tip clearance between fan blades
and shroud (inches)
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Analyze:Analyze Factors that Affect Performance
Use rstool to visually inspect interaction between all three design factors (distance, pitch, clearance) simultaneously
D M A I C
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Improve:Improve the Cooling Fan Performance
Use optimization to automate the task offinding the maximum airflow
fmincon function
D M A I C
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Improve:Improve the Cooling Fan Performance
Use uncertainty analysis to ensure a robust designTwo main contributors
Model uncertaintyManufacturing variability
D M A I C
Model noise 0.00 +/- 0.96 ft3/minDistance from radiator (d) 1.00 +/- 0.005 inchBlade pitch angle (p) 27.3 +/- 0.5 degreesBlade tip clearance (c) 1.00 +/- 0.005 inch
Factors Nominal Value and Tolerance
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Improve:Improve the Cooling Fan Performance
Use Monte Carlo simulation to determineimpact of these variations
Mean = 882 ft3 / minStd Dev = + 2 ft3 / min
D M A I C
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Control:Control the Manufacturing and Installation
Use Statistical Process Control (SPC)techniques to monitor andcontrol manufacturing andinstallation of the fan
D M A I C
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Summary
Continued emphasis on quality initiatives
Data analysis increasingly becoming anintegral part of the engineering design process
MATLAB product family cansupport these initiatives
©20
07 T
he M
athW
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, Inc
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Questions?
©20
07 T
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athW
orks
, Inc
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