计量型统计过程控制

1VariableStatisticalProcessControl计量型统计过程控制2LearningObjectives学习目的Uponcompletionofthismodule,theparticipantswillbeableto:完成对本模块的学习后，学员将能够：ConstructthefollowingControlCharts:建立下列控制图：Variables:•I-MR:IndividualsandMovingRange(个体与移动极差图)•Xbar&R:XbarandRange(均值与极差图)•Xbar&S:XbarandStandarddeviation(均值与标准差图)31I-MRChart:IndividualandMovingRangeChartI-MR图:个体和移动极差图2XBar-RChart:XbarandRangeChartXBar-R图:均值和极差图3XBar-SChart:XbarandStandardDeviationChartXBar-S图：均值和标准差图VariableControlCharts:计量型控制图:ControlChartTypes控制图类型7CreatingI–MRChartwithMinitab用Minitab创建I-MR图•I–MRChart:IndividualsandmovingRangeChart.Eachsubgroupismadeupbyasinglesample.I-MR:个体与移动极差图,也叫X-MR图,子群由单一的测量值组成•PlotI-MRChart画出:I-MR图8765432Subgroup1141312111098765IndividualValueMean=9.314UCL=13.04LCL=5.591543210MovingRangeR=1.4UCL=4.574LCL=0IandMRChartforC1CreatingI–MRChartwithMinitab用Minitab创建I-MR图91.Recordtheindividualmeasurementsforeachsubgroup为每个子群记录个体的测量值2.ComputetheMovingRangeforeachsubgroupstartingwithsubgroup2.MRequalstheRangeforthesubgroupandtheprevioussubgroup’svalue.从subgroup2开始为每个子群计算变动范围MR等于子群和当前子群值的变动范围。Subgroup2:MR=8.5-8.0=.5Subgroup3:MR=8.5-7.4=1.1Subgroup4:MR=10.5-7.4=3.1Sample1234567X88.57.410.59.311.110.4MR0.51.13.11.21.80.7CreatingtheI-MRControlCharts创建I-MR控制图103.ComputeX,theaverageofalloftheindividualvalues.XwillgivethecenterlineontheXchart.X=(8.0+8.5+7.4+10.5+9.3+11.1+10.4)=9.31计算X，所有个体值的平均值，X将会给出X图的中心线4.ComputeR,theaverageofalloftheMR’s.RwillgivethecenterlineontheMRchartR=(.5+.9+3.1+1.2+1.8+.7)=1.37计算R，所有MR‘S的平均值，R将会给出MR图的中心线Sample1234567X88.57.410.59.311.110.4MR0.50.93.11.21.80.71167CreatingtheI-MRControlCharts创建I-MR控制图11FormulaForI-MRChartCalculationI-MRChart控制限计算公式：MRChartMR图XChartX图UCLMR=D4RLCLMR=D3RUCLX=X+E2RLCLX=X－E2RInI-MRCharts,E2=2.66.Otherconstantsrefertothefollowtable.在I-MR图中,E2=2.66,公式中其它常数见下表或本节后附录.12Appendix:ControlChartConstants:X-MR附录：控制图表常数X-MRSubgroupSizenE2D3D4d222.660*3.2671.12831.772*2.5751.69341.457*2.2822.05951.290*2.1152.32661.184*2.0042.53471.1090.0761.9242.70481.0540.1361.8642.84791.0100.1841.8162.970100.9750.2231.7773.078145.CalculatetheControlLimits:计算控制限：FortheXchart:UCL=X+E2RLCL=X–E2RUCL=9.31+(2.66x1.37)LCL=9.31-(2.66x1.37)UCL=12.95LCL=5.67(Thecoefficientisalways2.66fortheXchart)(X图的系数通常为2.66)FortheMRchart:UCL=DRLCL=DR(D,Darebasedonn=2)UCL=3.267x1.37LCL=0x1.37UCL=4.48LCL=04433CreatingtheI-MRControlCharts创建I-MR控制图156.Plotthecentrelineandcontrollimitsinthe2charts.CompletetheXChartandMRChart.画出两个图的中心线和控制限，画出X图和MR图.0.71.81.23.10.90.5MR10.411.19.310.57.48.58X7654321Sample765432Subgroup1141312111098765IndividualValueMean=9.314UCL=13.04LCL=5.591543210MovingRangeR=1.4UCL=4.574LCL=0IandMRChartforC1CreatingtheI-MRControlCharts创建I-MR控制图16X-MRChartsApplicationswheresamplesizeforprocessmonitoringisn=1100%automatedinspectionandmeasurementproductionrateisveryslowrepeatabilityofmeasurementisnegligiblevariationwithinunit(e.g.rollofpaper)isnegligibleTheX-MRChart(orI-MRChart)isausefulcontrolchartifthecharacteristicisindependentlyandnormallydistributed.18TheXbar,RchartplotsaveragesandrangesXbar,R控制图画出均值和极差Xbar,RchartsenableprocessownerstoevaluatechangesincentraltendencyandstabilityusingsubgroupingXbar,R控制图使过程所有者使用子群体能够估计中心趋势和稳定性变化Xbar-RChartXbar-R图X,R19XbarChartXbar图VariablesControlChartsinvolvecontinuousvariables,whereinthestatisticsofinterestarecentraltendencyandvariability(dispersion)计量型控制图包括连续性变量，其中重要的统计量是中心趋势和变异（散布）。TheX-barChartmeasuresthecentraltendencyofthevariableovertime.Itusesthemean,orX-bar,fromsamplesofsizen.X-bar图测量随着时间推移的变量的中心趋势。它使用来自大小为n的样本的平均值，或X-bar。20VariablesControlCharts:theXbarChart计量型控制图：Xbar图Thecenterlineofthechartisrepresentedbythelong-termaverageoftheaverages,orX-doublebar图的中心线由平均值的长期平均水平或X-doublebar描绘出来Thecontrollimitsboundthe+3sigma,or99.7%confidenceintervalonthemean控制界限规定极差为+3sigma,或在平均值上的99.7%的置信区间nxsCLˆ3'21VariablesControlCharts:TheRange(R)Chart计量型控制图：极差(R)图TheRange,orRChartmonitorsthevariabilitywithinsubgroupovertime极差，或R图监控随着时间推移在子群体内部的变动Thecenterlineofthechartisrepresentedbythelong-termaverageoftheranges,orR-bar图的中心线由极差的长期平均水平或R-bar描绘出来Thecontrollimitsboundthe+3[sigmaoftherange]confidenceintervalontherange控制界限规定极差为在平均值上的+3[sigmaoftherange]的置信区间Rˆ3'RsCL22Example:openthe:“XBar-R.Mtw”,CreatingtheXbar-Rcharts例：使用文件“XBar-R.Mtw”,画XBar-R图.CreatingXbar&RChartwithMinitab用Minitab创建Xbar&R控制图23252015105Subgroup0151413121110SampleMeanMean=12.19UCL=14.38LCL=10.009876543210SampleRangeR=3.796UCL=8.026LCL=0Xbar/RChartforTestTimeCreatingXbar&RChartwithMinitab用Minitab创建Xbar&R控制图24CreatingtheXbar&RControlCharts创建Xbar&R控制图Ifallpointsshowonlyrandomvariation:如果所有的点只是显示出随机变化：Usethecalculatedcontrollimitsformonitoringthenext75orsosubgroups使用计算出的控制界限来监控紧接着的大约75个子集Iftheprocessisstillincontrol,re-calculatethecontrollimitsusingallofthedata(thenkeepthemthere)如果过程仍在控制之下，使用所有数据重新计算控制界限（然后将其保留在那里）25Ifpatternsindicatespecialcausesofvariation:如果图形样式显示出变异特殊原因：Ifanassignablecauseispresent如果存在可归因的原因Ifthecauserelatestoisolatedpoints,removethepoint(s)andrecalculate若该原因与孤立的点有关系，移除这些点并重新计算Ifabroaderpatternexi