6 sigma 简介

6 sigma

6sigma4sigma3015sigma16sigma1

6sigma

6sigma6sigma

Y=f(x)

Y=f(x)Question 2)XY

6sigmaCTQ

6sigma

6sigma6Sigma ProcessD-M-A-I-C5136SigmaD-M-A-I-C11

S(Total Sum of Squares):

(Unbiased Variance):Sn-1

or

(Parameter)Statistics)

SigmaSigmaSigmaStandard DeviationVariationSigmaSigmaDPUDefect Per Unit,PPM

SigmaSigma

TUSL or LSL)33Sigma

N6052N01270Z-

75Z=22ZUSLLSL

Z-701 XZorXZZ2.010.0228

Z- Z=3

Z-Z=6Z6

6 sigma1.5

6Sigma3.4PPMCp=2.0Cpk=1.5

4Block Diagram2.52.01.51.00.51 2 3 4 5 6PoorGoodPoorGoodZ stZ shift

4Block DiagramABCDWorld Top

Process MappingProcess MappingProcessProcess MappingProcessProcessProcess

ProcessKey ProcessYield, Cost, Cycle timeProcess Loss/Cycle time//FlowQFDQuality Function Deployment)QFDCTQ

QFD ProcessPartCTQCTQQFDQFDCTQ

FMEAFailure Modes & Effects Analysis)FMEAFMEA ProcessBrainstorming

80%20%

BrainstormingBrainstormingFree WheelingTeamIdeaRound RobinTeamIdeaCard MethodTeamIdea

BrainstormingIdeaIdeaIdeaLogic Tree(Structure Tree)Break-downMECEMECEMutually Exclusive and Collective Exhaustive)

Benefit[]/

Measurement

/Bottle Neck/Issue

Inch or

White NoiseWhite NoiseZ.st

Black NoiseBlack Noise

Line 123LineLine123456789Line1Line2Line3

Rational SubgroupRational SubgroupSubgroupSubgroupGrouping

Short-termCapability(6)Long-termCapability(3) SLSUltstststst4M

Six Sigmaor6

/Short Term Process Capability IndexZltltCpkZlt=3Cpk

Long Term Process Capability IndexZltltCpkZlt=3 Cpk

Gage R&RGage R&RBlindGage R&R

Gage R&R%ToleranceGage%Study Var20%ProcessGage R&R6 Project

Gage R&RGage R&RPartsgono go1V220

4%Gage R&R=[320] 100%=15%

Gage R&RGage R&RMinitabGage R&RGraphP39

Gage R&RP38

Gage R&RX bar50%Parts

Gage R&RR

Gage R&RNumber of Distinct Categories=44Categories324

Gage R&RNumber of Distinct CategoriesNumber of Distinct Categories01Number of Distinct Categories24Number of Distinct Categories5

Gage R&RGage R&RMinitabGage R&R Study-ANOVA Method

P36

Gage R&RR36

Gage R&R%Study VarGage R&R20%%ToleranceGage R&R

Gage R&RP35

Gage R&RGage R&RMinitabMonitor CoverSix Sigma ThemeSpec=2.31.53102

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

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%

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

Gage R&RGage R&R252-3102-3

Gage R&RLinearityGage1

Gage R&R

Gage R&RStabilityTime1

Gage R&RBiasAccuracy

Gage R&RRepeatability1Repeatability

Gage R&RReproduceability)Reproduceability213

Gage R&RGage R&R

Gage R&R6 Project

Gage20%Accept20%-30%Accept30%

Gage R&R/Spec10%=0.0200.002

Gage R&RSamplingSpec

Gage R&RGage R&RGage R&R StudyGage R&R Study3Repeatability(ReproduceabilityProcessSpec

Gage R&R Error

Gage R&RGage R&RGage R&RGageor YX

Rational SubgroupingRational Subgroup6 Sigma

Rational SubgroupX5MManMachine&MaterialLOTMethodMeasurement

Rational SubgroupingTV Back CoverRational SubgroupingXLotLot

SLSUKM

KK=0Cp=CpkMMid-rangeTTolerancneSUUpper SpecSLLower Spec

MinitabProjectXYX

MinitabP48

Submit CommandP49

MinitabP50

CpCpkCpuCplPpPpkPpuPplZstZlt

MinitabP51

MinitabP52

DDefectorDODefect Opportunity

UUnitDPUDefect Per UnitDPODefect Per OpportunityUnit

DPMODefect Per Million opportunity1,000,000DPO 1,000,000 Six SigmaPND=None DefectPND=1-DPO

DPU/DPO/DPMO/P(ND)10010010 DPU/DPO/DPMO/P(ND)DPU=D/UDPU=100/100=1.0100%1

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%)

YDPUre2.71828

r=0

Y=e-dpuY0

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%

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

YFT(First Time Yield)()YRT(Rolled Throughput Yield)

YNA(Normalized Yield)

VFTFirst Time Yield

A100Unit70%30%1515Final YieldYF[]85%First Time YieldYFTYFT70%

YRT(Rolled Throughput Yield)A3YRT/YND123YFT=80%YF=100%YFT=70%YF=90%YFT=90%YF=95%

YRFYFTYRT=0.80.70.9=0.504(50.4%)YND(Normalized Yield)n

YND(Normalized Yield)YFT=79.6%YND(Normalized Yield)SigmaYRF

Process Mapping

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

(YRT)MinitabP62

(YRT)MinitabP63

(YRT)MinitabP64

Analysis

GraphFocusingGraph

GraphGraphGraphGraph

GraphGraphMinitabCompressor333

GraphHistogramGraph>HistogramP67

GraphP67

GraphPlotGraph>PlotP68

GraphP68

GraphBox PlotGraph>Box PlotP69

GraphP69

GraphMatrix PlotGraph> Matrix PlotP70

GraphP70

Hypothesis TestFlatron MonitorLG Digital TVDigital TV6ToolTool019 PCS

Hypothesis Test(Null Hypothesis:Ho)or(Alternative Hypothesis:Hi)Ho

Hypothesis Test(Type Error:)(Type Error:)(Test Statistic)Ho(Significance Level)=0.05(or0.01,0.10)Ho

Hypothesis Test

Hypothesis Test[Sample()]Ho1=2Ho1=2=3=nHo 1=2Ho 1=2= 3 n

Hypothesis Test[]H112H11 2 1 2H11 2H11 2 1 2

Hypothesis TestZT-testF-test)F-test2x2(chi-Square)

Hypothesis Test/

Hypothesis Test(HoHi)=0.100.050.01ZTChi-squareP(Probability)(H1)P(Probability)(Ho)

Hypothesis Test(Ho) (H1)(Ho) (H1)()

Hypothesis Test(Ho)(Ho)0(Ho)0(Ho)MinitabP-Value(Ho)P-Value(Ho)

Hypothesis TestMinitabTransmission Housing10CTQ10CTQ8Fixture Brake&8FixtureFixureX

Hypothesis TestMinitabP76

Hypothesis TestP76

Hypothesis TestMinitab1P77

Hypothesis TestP77

Hypothesis TestP78

Hypothesis TestSampleTarget SampleTarget(Ho:H1Fixture 1Target Mean

Hypothesis TestP80

Hypothesis TestP81

Hypothesis TestX2Chi-squareGoodness of fit testorHoP1=P2==PnH1P1P2Pn50%

Hypothesis TestContingency TableHoH1)

Hypothesis TestEOX2Expected FrequencyObserved FrequencyX2

Hypothesis TestX2(Chi-square)3MonitorN=309Monitor4X2(Chi-square)(Ho)H1

Hypothesis TestABCD

Hypothesis TestHoH1

Hypothesis TestMinitabP84

Hypothesis TestP84

Improvement

ANOVAANOVAYXY

ANOVAY(Factor)(Level)(Sum of square)Balance/Unbalance

ANOVA One Way ANOVA21Balance ANOAV2 DoE=Design of Experiment

(Logic Tree)YnX63%Y

YGage R&R20%

XBlocking

Flow Chart&Process MappingRolled Through Yield

Blocking

10NoiseBlockingSample

Run Sample

NoiseNoise

BlockingBlockBlockingBlockingBlockingBlocking

Mechanism

GRAPHCapability AnalysisHistogramBox PlotParetoScatter PlotCube PlotMain effect plot&Interaction plot&

P-valueT-testF-testChi-square(ANOVA Tables(Regression)

1(A1:60A2:65A3:70A4:75312

(A)(Kg/mm2)

A1A2A3A48.448.599.348.928.368.919.418.928.288.609.698.74

MinitabP97

2(Yield%)(A)A1(180 )A2(190 )A3(200 ) A3(200 ) (B)B1MB2QB3P

A

BA1A2A3A4B197.698.699.098.0B297.398.298.097.7B396.796.997.996.5

MinitabP101

A3=200B1

(Factorial Design)nk2nn23nn3

(Factorial Design)22(A0A1)Mold(B0B1)(balance)4

(Factorial Design)

A0A1B031165821108872352517454643B1228430373829134218211823249486735

(Factorial Design)MinitabP106

(Factorial Design)P106

(Factorial Design)(mix)1mold-1mold(mix)Main effects plot

(Factorial Design)Interaction PlotP112

(mix,mold)

(Factorial Design)23XYXYXY

(Factorial Design)Cube plot

(Factorial Design)(mix)1mold-1mold

(Factorial Design)23FilterFilet2

(Factorial Design)Run22(Yield)221

(Factorial Design)

RUNTempTimeConc.Yield1-1-1-16521-1-1433-11-146.5411-1435-1-1159.561-11447-11151811143

(Factorial Design)MinitabP115

(Factorial Design)Main effects plotP120

(Factorial Design)Yieldtemp/time/concplot GraphLow Level(-1)[(-1)]High Level(1)[(+1)]

(Factorial Design)Interaction plotP121

(Factorial Design)Temp*TimeTemp*ConcTime*Conc

(Factorial Design)Cube plot4651606544434443temp-1-11timeconc11

(Factorial Design)temp(1)time(1)conc(1)temp(1)time(-1)conc(-1)

(Fractional factorial design)(Fractional factorial design)

(Fractional factorial design2n3n

(Fractional factorial design(Fractional factorial design)Screening/(Fractional factorial design)

(Fractional factorial design)25P124

(Fractional factorial design)253216X1X2X3X4X5=-1X1X2X3X4X5=+1

(Fractional factorial design)X1X2X3X4X5=+116

(Fractional factorial design)P125

(Fractional factorial design)2516222222

(Fractional factorial design-1-1+1X1+1-1+1X3X4-1+1X2-1+1X5

(Fractional factorial design423-123+or-42X3Z1X2

(Fractional factorial designX1X2X32X3 Column=X1 X2 ColumnX1 Column=X2 X3 ColumnX2 Column=X1 X3 Column-1-1+1X1+1-1+1X2X3

(Fractional factorial design255(liter/min)%RPM

(Fractional factorial design

(Fractional factorial designMinitabP129

(Fractional factorial designP129

(Fractional factorial designMain effects plotP135

(Fractional factorial designInteraction plotP136

(Fractional factorial designcatalyst*temperaturetemperature*concentrate 233

(Fractional factorial designCube plot67655655606952784945636110159395

(Fractional factorial design+12%+1180-13%

RegressionRegression/PointYXy=a+bx+error a= b=

Regression12112

RegressionRegreesion )?Vital FewYXY

RegressionVital Few

Regressionab

Regressionab0

RegressionXX

RegressionMinitabLOT

LOTX10203040405060607080Y2029506070859095109120

RegressionP141

RegressionP142

RegressionP143

RegressionP144

RegressionFITSYman-hour=4.17+1.48 lot sizeResidualerrorC4=C2-C3

RegressionResidualResidualPlotResidual0Residual(Normal Distribution)Residual

Regression

RegressionResidualP146

RegressionP146

RegressionP147

RegressionStat>Besic Stactistic>Normality Test Variable:Resi 1,Value=0.269

Regression(Residual) P148

Regressiony=a+bx,a=4.71b=1.48Constant P-ValueH00,0H10,0H04.710

RegressionP-ValueH0Lot size=orH1Lot size orP-Value=0.00SR-Sq

RegressionR-Sq(adj)Fitting

RegressionP150

RegressionP151

RegressionLOTXYR-Sq=98.5%R-Sq65%P-Value=0.269, Normality Test

(Control)

Projectprocessprocessprocess

//Process Foolproofproject

Six SigmaYCTQSystemsamplingKnow-how

Six SigmaMechanism

Six Sigma

Control ChartSPC=Statistical ProcessStatisticalprocessProcessControl

Control ChartSPC=Statistical ProcessWhite Noise(Black Noise

Control ChartProcessSubgroupProcessProcesssubgroupsubgroupProcess

Control ChartSPCStatistical Process Control)LogicOutputControllerProcessINPUTOUTPUTSAMPLENoise

Control ChartYSix SigmaInputY

Control ChartProcessOutputProcess

Control ChartProcessProcessoutput

Control ChartProcessoutput3

ProcessUCLXLCL

Control ChartControl Chart)

Control Chart

Control Chart3 99.73%2n6n=5

Control Chart& n

&X &R n

Control ChartMinitab10 Subgroup=25Subgroup Size=10=4.0341.045

Control ChartP61

Control ChartP162

Control Chart73.7127

Control ChartMinitabTeam97.1Flexible Time100

Control Chart

Control ChartP163

Control ChartP164

Control Chart1996Flexible Time39%18%

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

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

Control ChartA23D31+3D41-3d2d3

Control ChartRun253511002

Control ChartUCLCLLCL

Control Chart(Run)

Control Chart5Run6Run7RunUCLCLLCL

Control ChartCycleCLLCLUCL

Control ChartTrendUCLCLLCL

Control Chart32/3UCLCLLCL

Six Sigma ReviewReview

1)Field SVCYProcess Map, Logic Tree, Minitab

Six Sigma Review

2)YGRPIssueDataRational Subgroup PlansampleProcessReviewsamplesubgroupData

Six Sigma Review

3)MinitabY

Six Sigma Review

4)4-Block DiagramIssueZ.stZ.ltGraphYprocessgraph/Project issue&


1)XANOVAPareto DiagramScreening DOERegression

Six Sigma Review

2)XYPlotChart(CTQ)Box PlotRegressionANOVA(T-Test)Screeing DOEX

Six Sigma Review

3)CTQCTQProcessIssue


1)Regression/ANOVADOEoutputCube Plot YP-Value

Six Sigma Review

2)/specXRegressionCQTsampleRational Subgroup Plansample

Six Sigma Review

3)CTQYProcess OptimizationactionProcessDesign


1)DesignX&CTQYactionwhowhatwhenwherewhyhowchecksschedule

Documents

6 sigma 简介