6 sigma 简介
description
Transcript of 6 sigma 简介
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6 sigma
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6sigma4sigma3015sigma16sigma1
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6sigma
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6sigma6sigma
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Y=f(x)
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Y=f(x)Question 2)XY
6sigmaCTQ
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6sigma
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6sigma6Sigma ProcessD-M-A-I-C5136SigmaD-M-A-I-C11
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S(Total Sum of Squares):
(Unbiased Variance):Sn-1
or
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(Parameter)Statistics)
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SigmaSigmaSigmaStandard DeviationVariationSigmaSigmaDPUDefect Per Unit,PPM
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SigmaSigma
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TUSL or LSL)33Sigma
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60570
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N6052N01270Z-
75Z=22ZUSLLSL
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Z-701 XZorXZZ2.010.0228
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Z
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Z- Z=3
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Z-Z=6Z6
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6 sigma1.5
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6Sigma3.4PPMCp=2.0Cpk=1.5
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4Block Diagram2.52.01.51.00.51 2 3 4 5 6PoorGoodPoorGoodZ stZ shift
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4Block DiagramABCDWorld Top
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Process MappingProcess MappingProcessProcess MappingProcessProcessProcess
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ProcessKey ProcessYield, Cost, Cycle timeProcess Loss/Cycle time//FlowQFDQuality Function Deployment)QFDCTQ
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QFD ProcessPartCTQCTQQFDQFDCTQ
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FMEAFailure Modes & Effects Analysis)FMEAFMEA ProcessBrainstorming
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80%20%
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BrainstormingBrainstormingFree WheelingTeamIdeaRound RobinTeamIdeaCard MethodTeamIdea
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BrainstormingIdeaIdeaIdeaLogic Tree(Structure Tree)Break-downMECEMECEMutually Exclusive and Collective Exhaustive)
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Benefit[]/
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Measurement
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/Bottle Neck/Issue
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Inch or
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White NoiseWhite NoiseZ.st
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Black NoiseBlack Noise
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Line 123LineLine123456789Line1Line2Line3
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Rational SubgroupRational SubgroupSubgroupSubgroupGrouping
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Short-termCapability(6)Long-termCapability(3) SLSUltstststst4M
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Six Sigmaor6
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/Short Term Process Capability IndexZltltCpkZlt=3Cpk
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Long Term Process Capability IndexZltltCpkZlt=3 Cpk
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Gage R&RGage R&RBlindGage R&R
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Gage R&R%ToleranceGage%Study Var20%ProcessGage R&R6 Project
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Gage R&RGage R&RPartsgono go1V220
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4%Gage R&R=[320] 100%=15%
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Gage R&RGage R&RMinitabGage R&RGraphP39
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Gage R&RP38
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Gage R&RX bar50%Parts
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Gage R&RR
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Gage R&RNumber of Distinct Categories=44Categories324
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Gage R&RNumber of Distinct CategoriesNumber of Distinct Categories01Number of Distinct Categories24Number of Distinct Categories5
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Gage R&RGage R&RMinitabGage R&R Study-ANOVA Method
P36
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Gage R&RR36
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Gage R&R%Study VarGage R&R20%%ToleranceGage R&R
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Gage R&RP35
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Gage R&RGage R&RMinitabMonitor CoverSix Sigma ThemeSpec=2.31.53102
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P34
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Gage R&RGage R&RCTQSpec2.0000.015
12(1-212.0032.0010.00221.9982.0030.00532.0072.0060.00142.0011.9980.00351.9992.0030.004R=0.015
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Gage R&R= R/5=0.015/5=0.013=(5.15/1.19)(R)=4.33(0.003)=0.013=(0.0130.030100%=43.3%4.335.15/d* d*5.15Gage5.1599%
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d*
234511.411.912.242.4821.281.812.152.4031.231.772.122.3841.211.752.112.3751.191.742.102.3661.181.732.092.3571.171.732.092.3581.171.722.082.3591.161.722.082.34101.161.722.082.34
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Gage R&RGage R&R252-3102-3
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Gage R&RLinearityGage1
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Gage R&R
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Gage R&RStabilityTime1
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Gage R&RBiasAccuracy
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Gage R&RRepeatability1Repeatability
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Gage R&RReproduceability)Reproduceability213
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Gage R&RGage R&R
Gage R&R6 Project
Gage20%Accept20%-30%Accept30%
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Gage R&R/Spec10%=0.0200.002
Gage R&RSamplingSpec
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Gage R&RGage R&RGage R&R StudyGage R&R Study3Repeatability(ReproduceabilityProcessSpec
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Gage R&R Error
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Gage R&RGage R&RGage R&RGageor YX
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Rational SubgroupingRational Subgroup6 Sigma
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Rational SubgroupX5MManMachine&MaterialLOTMethodMeasurement
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Rational SubgroupingTV Back CoverRational SubgroupingXLotLot
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SLSU
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SLSUKM
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KK=0Cp=CpkMMid-rangeTTolerancneSUUpper SpecSLLower Spec
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SU
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MinitabProjectXYX
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P46
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P47
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P47
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MinitabP48
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Submit CommandP49
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MinitabP50
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CpCpkCpuCplPpPpkPpuPplZstZlt
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MinitabP51
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MinitabP52
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DDefectorDODefect Opportunity
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UUnitDPUDefect Per UnitDPODefect Per OpportunityUnit
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DPMODefect Per Million opportunity1,000,000DPO 1,000,000 Six SigmaPND=None DefectPND=1-DPO
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DPU/DPO/DPMO/P(ND)10010010 DPU/DPO/DPMO/P(ND)DPU=D/UDPU=100/100=1.0100%1
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DPO=D/(UOpp)DPO=100/(10010)=0.1(10%)110%DPMO=DPO1,000,000DPMO0.11,000,000 DPMOP(ND)=1-DPO=1-0.1=0.9(90%)
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YDPUre2.71828
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r=0
Y=e-dpuY0
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Process Yield75034DPU/DPO/DPMO/Yield/Sigma10DPU==34 750=0.0453DPO=()=34 (750 10)=0.00453YieldY=e-dpu=2.7138-0.045=0.9559=95.6%
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DPMO=DPO 1,000,000=0.0045 1,000,000=4,500PPM 45,000PPMSigma=Zinv(0.9556)+1.5(=1.71+1.5=3.21ZinvZ
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YFT(First Time Yield)()YRT(Rolled Throughput Yield)
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YNA(Normalized Yield)
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VFTFirst Time Yield
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A100Unit70%30%1515Final YieldYF[]85%First Time YieldYFTYFT70%
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YRT(Rolled Throughput Yield)A3YRT/YND123YFT=80%YF=100%YFT=70%YF=90%YFT=90%YF=95%
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YRFYFTYRT=0.80.70.9=0.504(50.4%)YND(Normalized Yield)n
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YND(Normalized Yield)YFT=79.6%YND(Normalized Yield)SigmaYRF
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Process Mapping
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YRF=Y1Y2Y3Y4 = 0.99[0.910.990.99]1/30.970.98 =0.9035YNA=(YRT)1/3=(0.9035)1/4=0.9749()=1-0.9749=0.02510.0251ZZ=1.96
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(YRT)MinitabP62
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(YRT)MinitabP62
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(YRT)MinitabP63
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(YRT)MinitabP64
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(YRT)MinitabP64
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Analysis
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GraphFocusingGraph
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GraphGraphGraphGraph
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GraphGraphMinitabCompressor333
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GraphHistogramGraph>HistogramP67
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GraphP67
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GraphPlotGraph>PlotP68
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GraphP68
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GraphBox PlotGraph>Box PlotP69
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GraphP69
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GraphMatrix PlotGraph> Matrix PlotP70
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GraphP70
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Hypothesis TestFlatron MonitorLG Digital TVDigital TV6ToolTool019 PCS
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Hypothesis Test(Null Hypothesis:Ho)or(Alternative Hypothesis:Hi)Ho
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Hypothesis Test(Type Error:)(Type Error:)(Test Statistic)Ho(Significance Level)=0.05(or0.01,0.10)Ho
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Hypothesis Test
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Hypothesis Test[Sample()]Ho1=2Ho1=2=3=nHo 1=2Ho 1=2= 3 n
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Hypothesis Test[]H112H11 2 1 2H11 2H11 2 1 2
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Hypothesis TestZT-testF-test)F-test2x2(chi-Square)
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Hypothesis Test/
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Hypothesis Test(HoHi)=0.100.050.01ZTChi-squareP(Probability)(H1)P(Probability)(Ho)
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Hypothesis Test(Ho) (H1)(Ho) (H1)()
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Hypothesis Test(Ho)(Ho)0(Ho)0(Ho)MinitabP-Value(Ho)P-Value(Ho)
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Hypothesis TestMinitabTransmission Housing10CTQ10CTQ8Fixture Brake&8FixtureFixureX
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Hypothesis TestMinitabP76
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Hypothesis TestP76
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Hypothesis TestMinitab1P77
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Hypothesis TestP77
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Hypothesis TestMinitab1P78
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Hypothesis TestP78
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Hypothesis TestMinitab1P79
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Hypothesis TestSampleTarget SampleTarget(Ho:H1Fixture 1Target Mean
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Hypothesis TestMinitab2P80
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Hypothesis TestP80
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Hypothesis TestP81
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Hypothesis TestX2Chi-squareGoodness of fit testorHoP1=P2==PnH1P1P2Pn50%
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Hypothesis TestContingency TableHoH1)
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Hypothesis TestEOX2Expected FrequencyObserved FrequencyX2
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Hypothesis TestX2(Chi-square)3MonitorN=309Monitor4X2(Chi-square)(Ho)H1
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Hypothesis TestABCD
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Hypothesis TestHoH1
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Hypothesis TestMinitabP84
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Hypothesis TestP84
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Improvement
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ANOVAANOVAYXY
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ANOVAY(Factor)(Level)(Sum of square)Balance/Unbalance
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ANOVA One Way ANOVA21Balance ANOAV2 DoE=Design of Experiment
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Y X &
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Y()X(
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(Logic Tree)YnX63%Y
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YGage R&R20%
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XBlocking
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Flow Chart&Process MappingRolled Through Yield
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Blocking
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2Y
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10NoiseBlockingSample
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Unit
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Run Sample
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NoiseNoise
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BlockingBlockBlockingBlockingBlockingBlocking
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3
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Mechanism
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GRAPHCapability AnalysisHistogramBox PlotParetoScatter PlotCube PlotMain effect plot&Interaction plot&
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P-valueT-testF-testChi-square(ANOVA Tables(Regression)
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//Y
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+/-2
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Cost
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YCTQ
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1(A1:60A2:65A3:70A4:75312
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(A)(Kg/mm2)
A1A2A3A48.448.599.348.928.368.919.418.928.288.609.698.74
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MinitabP97
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P97
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P98
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P98
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P99
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P99
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2(Yield%)(A)A1(180 )A2(190 )A3(200 ) A3(200 ) (B)B1MB2QB3P
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A
BA1A2A3A4B197.698.699.098.0B297.398.298.097.7B396.796.997.996.5
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MinitabP101
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P102
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P102
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P103
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P103
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A3=200B1
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(Factorial Design)nk2nn23nn3
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(Factorial Design)22(A0A1)Mold(B0B1)(balance)4
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(Factorial Design)
A0A1B031165821108872352517454643B1228430373829134218211823249486735
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(Factorial Design)MinitabP106
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(Factorial Design)P106
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(Factorial Design)P107
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(Factorial Design)P108
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(Factorial Design)P108
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(Factorial Design)P109
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(Factorial Design)P109
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(Factorial Design)P110
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(Factorial Design)P110
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(Factorial Design)P111
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(Factorial Design)(mix)1mold-1mold(mix)Main effects plot
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(Factorial Design)Interaction PlotP112
(mix,mold)
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(Factorial Design)23XYXYXY
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(Factorial Design)Cube plot
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(Factorial Design)(mix)1mold-1mold
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(Factorial Design)23FilterFilet2
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(Factorial Design)Run22(Yield)221
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(Factorial Design)
RUNTempTimeConc.Yield1-1-1-16521-1-1433-11-146.5411-1435-1-1159.561-11447-11151811143
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(Factorial Design)MinitabP115
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(Factorial Design)P115
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(Factorial Design)P116
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(Factorial Design)P117
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(Factorial Design)P117
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(Factorial Design)P118
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(Factorial Design)P118
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(Factorial Design)P119
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(Factorial Design)P119
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(Factorial Design)Main effects plotP120
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(Factorial Design)Yieldtemp/time/concplot GraphLow Level(-1)[(-1)]High Level(1)[(+1)]
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(Factorial Design)Interaction plotP121
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(Factorial Design)Temp*TimeTemp*ConcTime*Conc
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(Factorial Design)Cube plot4651606544434443temp-1-11timeconc11
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(Factorial Design)temp(1)time(1)conc(1)temp(1)time(-1)conc(-1)
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(Fractional factorial design)(Fractional factorial design)
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(Fractional factorial design2n3n
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(Fractional factorial design(Fractional factorial design)Screening/(Fractional factorial design)
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(Fractional factorial design)25P124
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(Fractional factorial design)253216X1X2X3X4X5=-1X1X2X3X4X5=+1
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(Fractional factorial design)X1X2X3X4X5=+116
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(Fractional factorial design)P125
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(Fractional factorial design)2516222222
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(Fractional factorial design-1-1+1X1+1-1+1X3X4-1+1X2-1+1X5
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(Fractional factorial design423-123+or-42X3Z1X2
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(Fractional factorial designX1X2X32X3 Column=X1 X2 ColumnX1 Column=X2 X3 ColumnX2 Column=X1 X3 Column-1-1+1X1+1-1+1X2X3
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(Fractional factorial design255(liter/min)%RPM
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(Fractional factorial design
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(Fractional factorial designMinitabP129
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(Fractional factorial designMinitabP129
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(Fractional factorial design
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(Fractional factorial designP129
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(Fractional factorial designP130
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(Fractional factorial designP131
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(Fractional factorial designP131
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(Fractional factorial designP132
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(Fractional factorial designP133
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(Fractional factorial designP133
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(Fractional factorial designP134
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(Fractional factorial designP134
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(Fractional factorial designMain effects plotP135
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(Fractional factorial design
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(Fractional factorial designInteraction plotP136
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(Fractional factorial designcatalyst*temperaturetemperature*concentrate 233
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(Fractional factorial designCube plot67655655606952784945636110159395
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(Fractional factorial design+12%+1180-13%
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RegressionRegression/PointYXy=a+bx+error a= b=
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Regression12112
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RegressionRegreesion )?Vital FewYXY
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RegressionVital Few
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Regressionab
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Regressionab0
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RegressionXX
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RegressionMinitabLOT
LOTX10203040405060607080Y2029506070859095109120
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RegressionP141
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RegressionP142
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RegressionP143
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RegressionP143
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RegressionP144
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RegressionFITSYman-hour=4.17+1.48 lot sizeResidualerrorC4=C2-C3
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RegressionResidualResidualPlotResidual0Residual(Normal Distribution)Residual
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Regression
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Regression
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Regression
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RegressionResidualP146
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RegressionP146
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RegressionP147
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RegressionP147
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RegressionStat>Besic Stactistic>Normality Test Variable:Resi 1,Value=0.269
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Regression(Residual) P148
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Regressiony=a+bx,a=4.71b=1.48Constant P-ValueH00,0H10,0H04.710
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RegressionP-ValueH0Lot size=orH1Lot size orP-Value=0.00SR-Sq
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RegressionR-Sq(adj)Fitting
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RegressionP150
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RegressionP151
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RegressionLOTXYR-Sq=98.5%R-Sq65%P-Value=0.269, Normality Test
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(Control)
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Projectprocessprocessprocess
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//Process Foolproofproject
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Six SigmaYCTQSystemsamplingKnow-how
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Six SigmaMechanism
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Six Sigma
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Control ChartSPC=Statistical ProcessStatisticalprocessProcessControl
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Control ChartSPC=Statistical ProcessWhite Noise(Black Noise
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Control ChartProcessSubgroupProcessProcesssubgroupsubgroupProcess
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Control ChartSPCStatistical Process Control)LogicOutputControllerProcessINPUTOUTPUTSAMPLENoise
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Control ChartYSix SigmaInputY
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Control ChartProcessOutputProcess
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Control ChartProcessProcessoutput
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Control ChartProcessoutput3
ProcessUCLXLCL
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Control ChartControl Chart)
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Control Chart
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Control Chart3 99.73%2n6n=5
- Control Chart& n
- &X &R n
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Control ChartMinitab10 Subgroup=25Subgroup Size=10=4.0341.045
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Control ChartP61
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Control ChartP162
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Control Chart73.7127
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Control ChartMinitabTeam97.1Flexible Time100
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Control Chart
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Control ChartP163
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Control ChartP164
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Control Chart1996Flexible Time39%18%
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Control ChartSPC
nA2A3D3D4B3B4d2d312.663.76------21.8802.65903.62703.6271.1280.85331.0231.95402.57502.5861.693088840.7291.62802.28202.2662.0590.66050.5771.42702.11502.0892.3260.864
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Control Chart
nA2A3D3D4B3B4d2d360.4831.28702.0040.0301.9702.5340.84870.4191.1820.0761.9240.1181.8822.7040.83380.3731.0990.1361.9640.1851.8152.8470.82090.3371.0320.1841.8160.2391.7612.9700.808100.3080.9750.2231.7770.2841.7163.0780.797
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Control ChartA23D31+3D41-3d2d3
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Control ChartRun253511002
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Control ChartUCLCLLCL
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Control Chart(Run)
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Control Chart5Run6Run7RunUCLCLLCL
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Control ChartCycleCLLCLUCL
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Control ChartTrendUCLCLLCL
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Control ChartUCLCLLCL
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Control ChartUCLCLLCL
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Control Chart32/3UCLCLLCL
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Control ChartUCLCLLCL
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Six Sigma ReviewReview
1)Field SVCYProcess Map, Logic Tree, Minitab
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Six Sigma Review
2)YGRPIssueDataRational Subgroup PlansampleProcessReviewsamplesubgroupData
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Six Sigma Review
3)MinitabY
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Six Sigma Review
4)4-Block DiagramIssueZ.stZ.ltGraphYprocessgraph/Project issue&
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Six Sigma ReviewReview
1)XANOVAPareto DiagramScreening DOERegression
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Six Sigma Review
2)XYPlotChart(CTQ)Box PlotRegressionANOVA(T-Test)Screeing DOEX
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Six Sigma Review
3)CTQCTQProcessIssue
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Six Sigma ReviewReview
1)Regression/ANOVADOEoutputCube Plot YP-Value
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Six Sigma Review
2)/specXRegressionCQTsampleRational Subgroup Plansample
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Six Sigma Review
3)CTQYProcess OptimizationactionProcessDesign
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Six Sigma ReviewReview
1)DesignX&CTQYactionwhowhatwhenwherewhyhowchecksschedule