Slide 1Why Bother?Taguchi Case StudyResults from Less VariationTaguichi Loss FunctionSlide 6Slide 7Definition of Robust DesignSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Factors That Have No EffectsAnother Source of Variance Effects: NonlinearitiesSummary of Variance EffectsRobust Design Approach, 2 StepsDesign ResolutionFractional FactorialsDesign ResolutionMinitab Explanation for Screening Run in LabHubcap Example of Propagation of ErrorsSlide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Robust DesignME 470Systems DesignFall 2010Why Bother?Customers will pay for increased quality!Customers will be loyal for increased quality!Taguchi Case Study•In 1980s, Ford outsourced the construction of a subassembly to several of its own plants and to a Japanese manufacturer.•Both US and Japan plants produced parts that conformed to specification (zero defects)•Warranty claims on US built products was far greater!!!•The difference? Variation•Japanese product was far more consistent!Results from Less Variation•Better performance•Lower costs due to less scrap, less rework and less inventory!•Lower warranty costsTaguichi Loss FunctionLossTargetTargetTraditional Approach Taguichi DefinitionWhy We Need to Reduce VariationCostLow Variation;Minimum CostLSLLSLUSLUSLNomNomCostHigh Variation;High CostLSLLSLUSLUSLNomNomCostNomNomOff target; minimum variabilityUSLUSLLSLLSLOff target; barely acceptable variabilityCostNomNomLSLLSLUSLUSLWhy We Need to Shift MeansDefinition of Robust DesignRobustness is defined as a condition in which the product or process will be minimally affected by sources of variation.A product can be robust against:–variation in raw materials–variation in manufacturing conditions–variation in manufacturing personnel–variation in the end use environment–variation in end-users–wear-out or deterioration646362616059585756Target USLLSLProcess Capability Analysis for Desired% Total% > USL% < LSL% Total% > USL% < LSLCpmPpkPPLPPUPpStDev (Overall)Sample NMeanLSLTargetUSL0.000.000.000.000.000.002.002.002.002.002.000.66660010060566064Expected PerformanceObserved PerformanceOverall CapabilityProcess DataIf your predicted design capability looks like this, you do not have a functional performance need to apply Robust Parameter Design methods. Cost, however, may still be an issue if the input (materials or process) requirements are tight!6462605856545250Target USLLSLProcess Capability Analysis for Y1% Total% > USL% < LSL% Total% > USL% < LSLCpmPpkPPLPPUPpStDev (Overall)Sample NMeanLSLTargetUSL47.40 0.0047.4049.00 0.0049.000.320.020.021.670.841.5782910056.10356.00060.00064.000Expected PerformanceObserved PerformanceOverall CapabilityProcess DataIf your predicted capability looks like this, you have a need to both reduce the variation and shift the mean of this characteristic - a prime candidate for the application of Robust Parameter Design methods.Variables or parameters which–affect system performance–are uncontrollable or not economical to controlExamples include–climate–part tolerances–corrosionNoise FactorsClasses of Noise FactorsNoise factors can be classified into:–Customer usage noiseMaintenance practiceGeographic, climactic, cultural, and other issuesDuty cycle–Manufacturing noiseProcessesEquipmentMaterials and part tolerances–Aging or life cycle noiseComponent wearCorrosion or chemical degradationCalibration drifOperating TemperaturePressure VariationFluid Viscosity Operator Variation50403020100124123122121120119118117116Observation NumberTemperature (deg C)Mean=120.1UCL=123.1LCL=117.050403020100100810041000996992Observation NumberPres sure (psia)1Mean=1000UCL=1007LCL=993.6504030201008281807978777675Observation Number% AMean=78.18UCL=81.15LCL=75.22504030201008070605040Observation NumberDiameter (Mils)I Chart for Diameter by OperatorMean=48.86UCL=58.50LCL=39.23Operator 1 Operator 2Countermeasures for NoiseIgnore them!–Will probably cause problems later onTurn a Noise factor into a Control factor–Maintain constant temperature in the plant–Restrict operating temperature range with addition of cooling systemISSUE : Almost always adds cost & complexity!Compensate for effects through feedback–Adds design or process complexityDiscover and exploit opportunities to shif sensitivity–Interactions–Nonlinear relationshipsHow to describe the Engineering System?Z1Z2...ZnY1Y2...YnX1X2...XnControlFactorsNoiseFactorsInputsOutputsSystemThe Parameter DiagramTraditional Approach to Variation ReductionReduce Variation in X’sWhat are the advantages and disadvantages of this approach?=f( )Y=f( )X1X2XnY X1X2XnLSLUSLClassifying Factors that Cause Variation in YVariation in Y can be described using the mathematical model:where Xn are Control Factors Zn are Noise FactorsssssssnnzzzxxxyS222222......2121Factors That Have No Effects•A factor that has little or no effect on either the mean or the variance can be termed an Economic Factor•Economic factors should be set at a level at which costs are minimized, reliability is improved, or logistics are improvedAMain Effects Plot2YSYAnother Source of Variance Effects: NonlinearitiesExpectedDistributionof YTwo Possible ControlConditions of AFactor A has an effect on both mean and varianceLow sensitivityregionHigh sensitivityregionSummary of Variance EffectsMean ShiftNoiseA - A + Variance ShiftNoiseA -A +Mean and Variance ShiftA +A -NoiseNon-linearityRobust Design Approach, 2 StepsStep 1Reduce the variability by exploiting the active control*noise factor interactions and using a variance adjustment factorStep 2Shif the mean to the target using a mean adjustment factor Factorial and RSM experimental designs are used to identify the relationships required to perform these activitiesVariance ShiftNoiseA -A +Mean ShiftNoiseB - B +Design Resolution•Full factorial vs. fractional factorial•In our DOE experiment, we used a full factorial. This can become costly as the number of variables or levels increases.•As a result, statisticians use fractional factorials. As you might suspect, you do not get as much information from a fractional factorial.•For the screening run in lab this week, we used a half-fractional factorial. (Say that fast 5 times!)Fractional FactorialsA Fractional Factorial Design is a factorial design in which