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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

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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)

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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

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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

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Questions?

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