Mar 21, 2016
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
60570
N6052N01270Z-
75Z=22ZUSLLSL
Z-701 XZorXZZ2.010.0228
Z
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
P34
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
SLSU
SLSUKM
KK=0Cp=CpkMMid-rangeTTolerancneSUUpper SpecSLLower Spec
SU
MinitabProjectXYX
P46
P47
P47
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)MinitabP62
(YRT)MinitabP63
(YRT)MinitabP64
(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 TestMinitab1P78
Hypothesis TestP78
Hypothesis TestMinitab1P79
Hypothesis TestSampleTarget SampleTarget(Ho:H1Fixture 1Target Mean
Hypothesis TestMinitab2P80
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
Y X &
Y()X(
(Logic Tree)YnX63%Y
YGage R&R20%
XBlocking
Flow Chart&Process MappingRolled Through Yield
Blocking
2Y
10NoiseBlockingSample
Unit
Run Sample
NoiseNoise
BlockingBlockBlockingBlockingBlockingBlocking
3
Mechanism
GRAPHCapability AnalysisHistogramBox PlotParetoScatter PlotCube PlotMain effect plot&Interaction plot&
P-valueT-testF-testChi-square(ANOVA Tables(Regression)
//Y
+/-2
Cost
YCTQ
1(A1:60A2:65A3:70A4:75312
(A)(Kg/mm2)
A1A2A3A48.448.599.348.928.368.919.418.928.288.609.698.74
MinitabP97
P97
P98
P98
P99
P99
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
P102
P102
P103
P103
A3=200B1
(Factorial Design)nk2nn23nn3
(Factorial Design)22(A0A1)Mold(B0B1)(balance)4
(Factorial Design)
A0A1B031165821108872352517454643B1228430373829134218211823249486735
(Factorial Design)MinitabP106
(Factorial Design)P106
(Factorial Design)P107
(Factorial Design)P108
(Factorial Design)P108
(Factorial Design)P109
(Factorial Design)P109
(Factorial Design)P110
(Factorial Design)P110
(Factorial Design)P111
(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)P115
(Factorial Design)P116
(Factorial Design)P117
(Factorial Design)P117
(Factorial Design)P118
(Factorial Design)P118
(Factorial Design)P119
(Factorial Design)P119
(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 designMinitabP129
(Fractional factorial design
(Fractional factorial designP129
(Fractional factorial designP130
(Fractional factorial designP131
(Fractional factorial designP131
(Fractional factorial designP132
(Fractional factorial designP133
(Fractional factorial designP133
(Fractional factorial designP134
(Fractional factorial designP134
(Fractional factorial designMain effects plotP135
(Fractional factorial design
(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
RegressionP143
RegressionP144
RegressionFITSYman-hour=4.17+1.48 lot sizeResidualerrorC4=C2-C3
RegressionResidualResidualPlotResidual0Residual(Normal Distribution)Residual
Regression
Regression
Regression
RegressionResidualP146
RegressionP146
RegressionP147
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 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 ChartUCLCLLCL
Control ChartUCLCLLCL
Control Chart32/3UCLCLLCL
Control ChartUCLCLLCL
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&
Six Sigma ReviewReview
1)XANOVAPareto DiagramScreening DOERegression
Six Sigma Review
2)XYPlotChart(CTQ)Box PlotRegressionANOVA(T-Test)Screeing DOEX
Six Sigma Review
3)CTQCTQProcessIssue
Six Sigma ReviewReview
1)Regression/ANOVADOEoutputCube Plot YP-Value
Six Sigma Review
2)/specXRegressionCQTsampleRational Subgroup Plansample
Six Sigma Review
3)CTQYProcess OptimizationactionProcessDesign
Six Sigma ReviewReview
1)DesignX&CTQYactionwhowhatwhenwherewhyhowchecksschedule