标准差的概念及应用

SILITEKCORPORATION1講師：程鈞尉/陳文博/楊晶晶No.：6S-HQ-AN-06-02-01SILITEKCORPORATION2◆什麼是六標準差？-統計上的涵義-方法論-六標準差技術的獨特賣點為何？◆六標準差在旭麗的推動方式◆妥善應付六標準差帶來的挑戰-開始接受挑戰-給予主管的叮嚀-給六標準差員工的叮嚀綱要SILITEKCORPORATION3什麼是六標準差？SILITEKCORPORATION4SixSigma有多小?SigmaDPPM拼錯字6s0.0025s0.57424s63.373s2,7002s45,5001s317,310小型圖書館所有書籍中僅一錯字大型圖書館所有書籍中僅一錯字大英百科全書中僅一錯字一本書中每30頁僅一錯字一本書中每1.5頁僅一錯字一本書中每頁錯5個字SILITEKCORPORATION5何谓s(标准差)？Thisisa6SigmaProcess(orZ=6)p(d)123456s反曲点(PointofInflexion)USL1smΣn(μ-Xi)2i=1nσ=SILITEKCORPORATION6s=15分→s=5分6σ通勤Y：影響通勤的問題Y=f（X）σ：變異！如何把15分鐘縮減到5分鐘？1234561ssUSLmLSL28:008:309:001p(d)sμUSL=ZX1=塞車X2=交通號誌X3=交通工具X4X5...SILITEKCORPORATION7如果我們充份瞭解與掌握X,為何我們要持續測試與檢驗Y?Y相依(Dependent)輸出(Output)結果(Effect)不良結果(Symptom)監測(Monitor)X1...Xn互相獨立(Independent)輸入(Input-Process)原因(Cause)問題(Problem)控制(Control)f(X)Y=專注於X而非YSixSigma焦點為了獲得好的結果,我們是否要專注於Y或X的行為?SILITEKCORPORATION8精密度vs.準確度準確度(Accuracy)精密度(Precision)YesNoYesNoaCpCSILITEKCORPORATION9準確度：精密度：=100%2TμXssˆ6ˆ6LSLUSLCp==規格公差製程能力指標：是綜合和二數值之指標。pkCaCpCpkC=(1-)xaCpC%100=規格公差/2規格中心值實際中心值aCSILITEKCORPORATION10Time3Time2Time1UpperSpecSpec(MadeupofRationalSubgroups)LowerLongTerm(Wider)Time4ShortTerm飛機跑道降落地點的分布SILITEKCORPORATION116sUSLLSL6s3.4DPPM~0DPPM1.5sshift06sprocesscapability4.5sZST-ShiftFactor=ZLT(6.0s)(1.5s)(4.5s)Z被定義為從平均數到規格界限(USL或LSL)之間這段距離里能放入的s個數SILITEKCORPORATION12SixSigma的品質水準•0.002DPPM,Cp=2理想的狀況(無偏移Ca=0)中心值±1.5s的偏移3.4DPPM,Cpk=1.5或用DPMO(DefectsPerMillionOpportunities)表示SILITEKCORPORATION13Cpk與Z值之間的關係Z=3Cpk當已知ZST-1.5=ZLT將Z=3Cpk代入上式3CpkST-1.5=3CpkLT兩邊除於3,則形成下列關係式：CpkST-0.5=CpkLT(2.0)(1.5)ST:短期(限量試產)LT:長期(大量生產)按定義,Z值是等於3倍的Cpk值SILITEKCORPORATION143.45.48.513213248721081592333374836879681,3501,8662,5553,4674,6616,2108,19810,72413,90317,86422,75028,71635,93044,56566,80793.3%91.9%90.3%88.5%86.4%84.1%81.6%78.8%75.8%72.6%69.1%65.5%61.8%57.9%54.0%50.0%46.0%42.1%38.2%34.5%30.9%27.4%24.2%21.2%18.4%15.9%13.6%11.5%9.7%8.1%1.51.471.441.401.371.341.301.271.241.201.171.141.101.071.041.000.970.940.900.870.840.800.770.730.700.670.630.600.570.530.500.470.430.400.370.330.300.270.230.200.170.130.100.070.030.00-0.03-0.07-0.10-0.13-0.17-0.20-0.23-0.27-0.30-0.33-0.37-0.40-0.43-0.47SigmaLevel(ZST)vs.DPPMTable(1.5sShift)1.000.970.930.900.870.830.800.770.730.700.670.630.600.570.530.500.470.430.400.370.330.300.270.230.200.170.130.100.070.032.001.981.951.901.871.850.801.771.751.701.671.651.601.571.541.51.471.441.401.371.341.301.271.231.201.171.131.101.071.0399.99966%99.99946%99.99915%99.99866%99.9979%99.9968%99.9952%99.9928%99.9892%99.984%99.977%99.966%99.952%99.931%99.90%99.87%99.81%99.74%99.65%99.53%99.38%99.18%98.9%98.6%98.2%97.7%97.1%96.4%95.5%94.5%6.05.95.85.75.65.55.45.35.25.15.04.94.84.74.64.54.44.34.24.14.03.93.83.73.63.53.43.33.23.13.02.92.82.72.62.52.42.32.22.12.01.91.81.71.61.51.41.31.21.11.00.90.80.70.60.50.40.30.20.166,80780,75796,801115,070135,666158,655184,060211,855241,964274,253308,538344,578382,089420,740460,172500,000539,828579,260617,911655,422691,462725,747758,036788,145815,940841,345864,334884,930903,199919,243ZSTCpSTDPPMLTYieldLTCpkLTZSTCpSTDPPMLTYieldLTCpkLTSILITEKCORPORATION15六標準差的方法論SILITEKCORPORATION16WhatIsSixSigma?MethodologySILITEKCORPORATION17VOCCTQDefineY=f（X1,X2,X3,…）MeasureAnalyzeImproveControlWhatIsSixSigma?TerminologyVOC(VoiceOftheCustomer)-ClarifycustomerrequirementsCTQ(CriticalToQualitycharacteristic)-CustomerperformancerequirementofaproductorserviceY-IdentifyCTQsXs-AffectvariablefactorSILITEKCORPORATION18•凝聽顧客的聲音（VOC）•選擇專案•成立專案小組•確認CTQs-Y1DiscussionofcharterSIPOCmapVOCdataOtherchartsdepictinggapTarget}GapCharterPurposeDeliverablesTextTYPICALGRAPHICSstep界定(Define)SILITEKCORPORATION19•定義衡量指標($?)•衡量系統驗證InterpretationsofdataandgraphicsParetochartshowingrelativeimportanceofdifferentcomponentsoftheproblemFrequencyplot(Histogram)showingpatternsindistributionandprocesssigmacalculationsTimeplotorControlchartshowingpatternsinvariationovertimeFlowchartdepictingcurrentprocesss=1.4ProcessshiftVANVATextTypicalGraphics2Step衡量(Measure)SILITEKCORPORATION20•定義不良•基準線•設定目標•確認X’sReasonsforselectingcausesforverificationInterpretationofverificationdataScatterplot,Stratifiedfrequencyplots,orTablesshowingverificationdataC&Ediagram(orothertoolshowingpotentialcausesidentified)XYABTextTypicalGraphics3Step分析(Analyze)SILITEKCORPORATION21•發現和確認-重要的少數X’s•效果測試(PilotSolution)Y=f(x)TextTypicalGraphicsExplanationsofcriteriaCommentsonplansandtestsResultsofpilottestsSolutionmatrixshowingrankedcriteriaandscoringforeachsolutionoptionPlansimplementationABCD4132forTeststartsInterpretationofanalysisofresultsandmethodsBeforeandAfterDatacomparingresultsofimplementationwithdataalreadycollectedinSteps1,2,or3.Plotsshouldbedrawntosamescale.σ=1.4σ=3.6TestFullscaleOriginalStep45改善(Improve)SILITEKCORPORATION22•確認效果持續性TextTypicalGraphicsCommentsontrainingplansandongoingmonitoringresponsibilitiesSummaryoflearningsandsuggestionsfornextstepsPlansforcelebrationandrecognitionSamplesofstandardizationdocumentationincludingrevisedflowcharts,QCProcesscharts,etc.LearningsChartsshowingareasthatstillneedimprovement67Step控制(Contr