测量系统分析用图

4．附图图4-1.1测量系统分辨力对过程分析和控制的影响数据组数与过程的分析测量数据对分析的影响测量数据对控制的影响1个数据组1个数据组不能用于对过程的参数估计或计算过程能力指数,仅能表明过程的输出是否合格只有下列条件下才可用于控制:·与规范相比过程变差较小·预期过程变差上的损失函数很平缓·过程变差的主要原因导致均值偏倚2~4个数据组2~4个数据组仅能提供粗糙的估计值,一般说来不能用于对过程的参数估计或计算过程能力指数·依据过程分布可用半计量控制技术·可产生不敏感的计量控制图5个及以上数据组5个及以上数据组能够用于过程参数估计,以及可以用于各种类型的控制图.表明测量系统具有足够的分辨力·可用于计量控制图图4-1.2过程波动的主要来源及测量系统分析的主要内容再现性再现性观测到的波动（总波动）过程的波动测量系统波动过程长期波动过程短期波动样本内波动量具的波动操作者的波动准确度或偏倚重复性线性稳定性分辨力★★图4-1.3测量系统分析实施流程图超过本手册的范围测量是否已准备?否超过本手册的范围测量是否已准备?否是是测量是否任意分配?测量是否任意分配?否否是是计数型量具研究(小样法)否是否有不同的测量仪器?否计数型量具研究(小样法)否是否有不同的测量仪器?否件?是是极差法是极差法是否计数型量具研究(大样法)是否有不同的测量仪器?否计数型量具研究(大样法)是否有不同的测量仪器?否否短期适用的分析时间?是短期适用的分析时间?是均值和极差或方差分析法图表分析长期均值和极差或方差分析法图表分析长期图4-1.4重复性极差控制图2名评价人3次试验5个零件评价人1评价人26.46.4UCLUCL2.52.5RR0.00.01234512345极差受控—测量过程是—致的图4-1.5零件评价人均值图2名评价人3次试验5个零件评价人1评价人2219.2219.2UCL控制上限UCL控制上限216.6216.6123451234530%的零件平均值在限值外，测量过程不足以检出零件间变差图4-1.6基准值基准值偏倚观测的平均值观测的平均值图4-2重复性重复性重复性重复性操作者B操作者C操作者B操作者C操作者A再现性图4-4稳定性时间2时间1图4-5a线性基准值基准值偏倚较小偏倚较大观测的平均值观测的平均值范围的较低部分范围的较高部分图4-5b线性（变化的线性偏倚）有偏倚有偏倚倚偏有观测的平均值无偏倚基准值图4-6偏倚示例基准值.80基准值.80Xbar=.75图4-7:量具重复性和再现性数据表格(包括零件内变差)零件评价人平均值12345评价人试验次数最大最小极差最大最小极差最大最小极差最大最小极差最大最小极差1.A1.68.58.101.07.93.14.87.78.09.97.83..14.58..42.162.2..67.57.101.08.92.16.85.77.08.96.81.15.59.40.193.34.平均值(全部).6251.00081750.89250.49750.76655.极差0.010.010.01.010..020.020.010.010.01.02.01.01.02.030.0136.B1.59.51.081.08.92.16.82.73.09.84.71.13.49.31.187.2.60.50.101.07.93.14.81.75.06.85.70.15.48.32.168.39.平均值(全部).551.007878.40.700510.极差0.010.010.020.010.010.020.010.020.030.010.010.020.010.010.020.01111.C1.56.49.071.10.95.15.84.77.07.87.74.13.56.39.1712.2.55.47.081.08.94.14.84.76.08.88.73.15.57.38.1913.314.平均值(全部).521.02.80.80.48.722515.极差.01.02.01.02.01.01.00.01.01.01.01.02.01.010.20.011零件平均值(xbarP)0.5651.007.799.824.459Rp=.55WIV平均值(xbarWIV)0.090.150.080.140.17RxbarWIV=.0918.Rbarbar=∑极差（行5+行10+行15）/极差数量=0.35/30=0.0117(只有最大/最小极差)19．[最大xbar=0.7665]-[最小x=0.7005]=R0=XbarDIFF=0.066≈0.0720．[Rbarbar=]×[D4*=]=UCLR21．[Rbarbar=]×[D3*=]=LCLR*试验次数为2次时D4=3.27，试验次数为3次时D4=2.58；7次试验以内D3=0。UCLR，LCLR代表单个R的极限。圈出那些超出限值的值，辨别原因并纠正。同一评价人采用最初仪器重复这些读数或剔除这些超限值并由其余观测值再次平均并计算R和极限值。注：图4-8:量具重复性和再现性报告(包括零件内变差)零件名称：零件号：日期：年月日量具名称：量具编号：量具类型：测量参数：尺寸规格：执行人：根据数据表：Rbarbar=0.0117XbarDIFF=0.07RP=0.55测量系统分析%总变差（TV）重复性—设备变差（EV）EV=Rbarbar×K1=0.0117×4.56=0.0534%EV=100[EV/TV]=100[.0534/1.178]=4.2%试验次数K1234.563.05再现性—评价人变差（AV）AV=[(XbarDIFF×K2)2-(EV2/nm)]1/2=((0.07×2.70)2–(0.052/5×2)1/2=0.178%AV=100[AV/TV]=100[0.178/1.178]=15.3%n=零件数量m=试验次数评价人23K3.652.70重复性和再现性(GR&R)GR&R=[(EV2+AV2)]1/2=(0.052+0.182)1/2=0.187%GR&R=100[GR&R/TV]=100[.187/1..178]=15.9%零件数K323456789103.652.702.302.081.931.821.741.671.62零件变差（PV）PV=RP×K3=0.55×2.08=1.144%PV=100[PV/TV]=100[1.144/.1.178]=97%零件内变差（WIV）WIV=xbarbarWIV+[(RXbarWIV×K3)2-(EVWIV)2/nWIVm]1/2/2=0.126+[(0.1872)2-0.0762/(3×2)]/2=0.218式中：xbarbarwiv=[∑xwiv(行17)]/xwiv读数数量=0.63/5=0.126nWIV=评价人数量,m=试验次数,EVWIV=[∑Rrge(行5,10,15)]/Rrge读数数量×K1=0.25/15×4.56=.076RRGE读数数量%WIV=100[WIV/TV]=100[0.22/1.179]=18.7%总变差(TV)TV=(GR&R2+PV2+WIV2)1/2=[(0.18)2+(1.144)2+(0.218)2]1/2=1.178图4-9:重复性极差控制图工厂×××部门×××操作人××××××计算日期控制极限工程规范×至×mm零件号机器编号×××日期×-×至×-×被测参数×××，××דה样本容量/频率零件名称×/×小时xbarbar=UCL=LCL=平均值(xbar图)1.11.00.90.80.70.6.0.50.4Rbar=UCLLCL=*极差（R图）UCLR=.130.130.12评价人A评价人B评价人C0.110.100.090.080.070.060.05R=.040.040.030.020.01日期时间读数12345和Xbar=和/读数数量R=最高-最低图4-10:零件评价人均值图工厂×××部门×××操作人××××××计算数据控制极限工程规范×至×mm零件号机器编号×××日期×-×至×-×被测参数×××，××דה样本容量/频率零件名称×/×小时xbarbar=0.8008UCL=0.876LCL=0.7256平均值(xbar图)1.1[评价人A][评价人B][评价人C]1.00.9UCL×0.8LCL0.70.60.50.4Rbar=UCLLCL=*极差（R图）0.130.120.1173%的零件平均值在限值外0.100.090.080.070.060.050.040.030.020.01日期时间读数12345和X=X=和读数数量R=最高-最低图4-11:标准均值和极差法量具重复性和再现性数据表评价人/试验次数零件平均值123451.A10.651.000.850.850.552.20.601.000.800.950.453.34.平均值0.6251.000.8250.8750.50xbara=0.76505.极差0.550.000.050.100.10Rbara=0.066.B10.551.050.800.800.407.20.550.950.750.750.408.39.平均值0.551.000.7750.7750.40xbarb=0.700010.极差0.000.10.050.050.00Rbarb=0.0411.C10.501.050.800.800.4512.20.551.000.800.800.5013.314.平均值0.5251.0250.800.800.475xbarc=0.725015.极差0.050.050.000.000.05Rbarc=0.03--零件--平均值(xbarP)0.5661.0080.800.8170.458xbar=0.730Rp=0.55----17.[Rbara=0.06]+[Rbarb=0.04]+[Rbarc=0.03]/[评价人数=3]Rbarbar=0.043318．[最大x=0.7650]-[最小x=0.70]=XbarDIFF=0.065≈0.0719.[Rbarbar=]×[D4*=]=UCLR20.[Rbarbar=]×[D3*=]=LCLR2次试验时D4=3.27，3次试验时D4=2.58。7次试验以内D3=0；UCLR，LCLR代表单个R的极限。圈出那些超出极限的值。查明原因并纠正。同一评价人采用最初的仪器重复这些读数或剔除这些值并由其余观测值再次平均并计算R和极限值。注：图4-12:标准均值和极差法量具重复性和再现性报告零件名称：零件号：日期：年月日量具名称：量具编号：量具类型：测量参数：尺寸规格：执行人：来自数据表：Rbarbar=0.0433XbarDIFF=0.07RP=0.55测量系统分析%总变差（TV）重复性—设备变差（EV）EV=Rbarbar×K1=0.0433×4.56=0.1976≈0.20%EV=100[EV/TV]=100[0.2/1.175]=17.0%试验次数K1234.563.05再现性—评价人变差（AV）AV=[(XDIFF×K2)2-(EV2/nm)]1/2=[(0.07×2.70)2-(0.202/5×2)]]1/2=0.178≈0.18%AV=100[AV/TV]=100[0.18/1.175]=15.3%n=零件数量m=试验次数评价人23K3.652.70重复性和再现性(GR&R)GR&R=(EV2+AV2)1/2=(0.202+0.182)1/2=0.269%GR&R=100[GR&R/TV]=100[0.269/1.175]=22.9%零件数K323456789103.652.702.302.081.931.821.741.671.62零件变差（PV）PV=RP×K3=0.55×2.08=1.144%PV=100[PV/TV]=100[1.144/1.175]=97.4%总变差（TV）TV=（GR&R2+PV2）1/2=(0.2692+1.1442)1/2=1.175(带有量具误差分量时为1.172)所有计算都基于预期5.15σ(在正态分布曲线之下99.0%的面积)。K1为5.15/d2*，d2*取决于试验次数（m）和零件数与评价人数的乘积（g），并假设该值大于15。d2*数值来自表2。AV—如果计算中根号下出现负值，评价人变差缺省为0。K2为5.15/d2*，式中d2*取决于评价人数量（m）和（g），g为1，因为只有单极差计算。K3为5.15/d2*，式中d2*取决于零件数（m）和（g），g为1，因为只有单极差计算。d2*来自D3，“质量控制和工业统计”A.J.Duncan图4-13线性图1名评价人12次试验5个零件过程变差=6.001.201.000.801.201.000.800.600.400.20-0.00-0.20-0.40-0.60++偏倚倚+++低++偏倚倚+++4.006.008.0010.004.006.008.0010.00偏倚=0.05线性=0.79拟合优度(R2)=0.98%线性=13.17图4-14:量具特性曲线接受概率1.000.900.800.700.600.500.400.300.200.100.000.600.801.001.021.04基准零件测量GRR=0.07偏倚=0.05图4-15绘制在正态概率纸上的量具特性曲线一Ⅱ偏倚0.0023偏倚0.0023低%高%-0.01610302040299.899.5969895908070605040302010510.50.2·······0.20.5125506070809095969899.599.8REPEA/重复性=0.0079未调整-0.014-0.012-0.010-0.00810302040299.899.5969895908070605040302010510.50.2·······0.20.5125506070809095969899.599.8REPEA/重复性=0.0079未调整被测零件的基准值图4-16:量具特性曲线0.90.60.70.81.0接受概率上限下限0.90.60.70.81.0接受概率上限下限0.00.10.20.30.40.5-0.015-0.010-0.0050+0.005+0.010+0.0150.00.10.20.30.40.5被测零件的基准值5．附表表5-1平均极差分布的d2*值（d2*值g>15）mg23456789101112131415161718192011.411.912.242.482.672.832.963.083.183.273.353.423.493.553.613.663.713.763.8121.281.812.152.402.602.772.913.023.133.223.303.383.453.513.573.633.683.733.7731.231.772.122.382.582.752.893.013.113.213.293.373.433.503.563.613.663.713.7641.211.752.112.372.572.742.883.003.103.203.283.363.433.493.553.613.663.713.7551.191.742.102.362.562.732.872.993.103.193.283.353.423.493.553.603.663.703.7561.181.732.092.352.562.732.872.993.103.193.273.353.423.493.553.603.653.703.7571.171.732.092.352.552.722.872.993.103.193.273.353.423.483.543.603.653.703.7581.171.722.082.352.552.722.872.983.093.193.273.353.423.483.543.603.653.703.7491.161.722.082.242.552.722.862.983.093.183.273.353.423.483.543.603.653.703.74101.161.722.082.342.552.722.862.983.093.183.273.343.423.483.543.603.653.703.74111.161.712.082.342.552.722.862.983.093.183.273.343.413.483.543.593.653.703.74121.151.712.072.342.552.722.852.983.093.183.273.343.413.483.543.593.653.703.74131.151.712.072.342.552.712.852.983.093.183.273.343.413.483.543.593.653.693.74141.151.712.072.342.542.712.852.983.083.183.273.343.413.483.543.593.653.693.74151.151.712.072.342.542.712.852.983.083.183.263.343.413.483.543.593.653.693.74161.151.712.072.342.542.712.852.983.083.183.263.343.413.483.543.593.643.693.74171.151.712.072.342.542.712.852.983.083.183.263.343.413.483.543.593.643.693.74181.151.712.072.332.542.712.852.983.083.183.263.343.413.483.543.593.643.693.74191.151.702.072.332.542.712.852.983.083.183.263.343.413.483.543.593.643.693.74201.141.702.072.332.542.712.852.983.083.183.263.343.413.483.543.593.643.693.74>201.1281.6932.072.3262.5342.7042.8472.9073.0783.1733.2583.3363.4073.4723.5323.5883.6403.6893.735表5-2:控制图常数子组内观察次数A2D3D4d221.88003.2671.12831.02302.5751.69340.72902.2822.05950.57702.1152.32660.48302.0042.53470.4190.0761.9242.70480.3730.1361.8642.84790.3370.1841.8162.970100.3080.2231.7773.078110.2850.2561.7443.173120.2660.2841.7163.258130.2490.3081.6923.336140.2350.3291.6713.407150.2230.3481.6523.472表5-3：量具研究(极差法)零件评价人A评价人B极差R=xmax-xmin10.850.800.0520.750.700.0531.000.950.0540.450.550.1050.500.600.10平均极差（Rbar）=∑Ri/5=0.35/5=0.07GR＆R=5.15（Rbar）/d2*=5.15（R）/1.19=5.15（0.07）/1.19=0.303过程变差=0.40%GR＆R=100[GR＆R/过程变差]=100[0.303/0.40]=75.5%表5-4：量具重复性和再现性数据评价人/试验次数零件平均值123456789101.A10.651.000.850.850.551.000.950.851.000.602.20.601.000.800.950.451.000.950.801.000.703.34.平均值0.6251.0000.8250.9000.5001.0000.9500.8251.0000.650xbara=0.82755.极差0.050.000.050.100.100.000.000.050.000.10Rbara=0.0456.B10.551.050.800.800.401.000.950.751.000.557.20.550.950.750.750.401.050.900.700.950.508.39.平均值0.5501.0000.7750.7750.4001.0250.9250.7250.9750.525xbarb=0.767510.极差0.000.100.050.050.000.050.050.050.050.05Rbarb=0.04511.C10.501.050.800.800.451.000.950.801.050.8512.20.551.000.800.800.501.050.950.801.050.8013.314.平均值0.5251.0250.8000.8000.4751.0250.9500.8001.0500.825xbarc=0.827515.极差0.050.050.000.000.050.050.000.000.000.05Rbarc=0.030--16零件平均值--(xbarP)0.5671.0080.8000.8250.4581.0170.9420.7831.0080.667xbar=0.8075Rp=0.559----17.[Rbara=0.045]+[Rbarb=0.045]+[Rbarc=0.03]/[#评价人数=3]Rbarbar.=0.0418．[Maxx=0.8275]-[Minx=0.7675]=xbarDiff0.0619.[Rbarbar=0.04]×[D4*=3.27]=UCLR0.1320.[Rbarbar=0.04]×[D3*=0.00]=LCLR0.00*2次试验时D4=3.27，3次试验时D4=2.58。7次试验以内D3=0；UCLR，LCLR代表单个R的极限。圈出那些超出极限的值。查明原因并纠正。同一评价人采用最初的量规仪器重复这些读数或剔除这些值并由其余观测值再次平均，计算R和极限值。注：表5-5：量具重复性和再现性报告零件号和名称：量具名称：厚薄规日期：4/12/88测量参数：厚度量具编号：X-29.34执行人：尺寸规格：0.6-1.0mm量具类型：0.0-10.1来自数据表：Rbarbar=0.044xbarDIFF=0.06RP=0.559测量系统分析%总变差（TV）重复性—设备变差（EV）EV=Rbarbar×K1=0.044×4.56=0.18%EV=100[EV/TV]=100[0.18/0.93]=18.7%试验次数K1234.563.05再现性—评价人变差（AV）AV=[(XbarDIFF×K2)2-(EV2/nm)]1/2=[(0.06×2.70)2-0.182/(10×2)]]1/2=0.16%AV=100[AV/TV]=100[0.16/0.93]=16.8%n=零件数量m=试验次数评价人23K3.652.70重复性和再现性(GR&R)GR&R=(EV2+AV2)1/2=(0.182+0.162)1/2=0.24%GR&R=100[R&R/TV]=100[0.24/0.93]=25.2%零件数K323456789103.652.702.302.081.931.821.741.671.62零件变差（PV）PV=RP×K3=0.56×1.62=0.90%PV=100[PV/TV]=100[0.90/0.93]=96.8%总变差（TV）TV=（R&R2+PV2）1/2=(0.242+0.902)1/2=0.93所有计算都基于预期5.15σ(在正态分布曲线之下99.0%的面积)。K1为5.15/d2*，d2*取决于试验次数（m）和零件数与评价人数的乘积（g），并假设该值大于15。d2*数值来自表2。AV—如果计算中根号下出现负值，评价人变差缺省为0。K2为5.15/d2*，式中d2*取决于评价人数量（m）和（g），g为1，因为只有单极差计算。K3为5.15/d2*，式中d2*取决于零件数（m）和（g），g为1，因为只有单极差计算。d2*来自D3，〈质量控制和工业统计〉A.J.Duncan表5-6：量具重复性和再现性报告一垫片示例量具R&R均值和极差法3位评价人，10个零件，2次试验评注：特殊研究5.15%总变差标准偏差重复性0.1818.7再现性0.1616.8量具R&R0.2425.2零件间0.9096.8基于本过程，量具合格注：容差=不适用总变差=0.93不同数据分级数=5置信水平CL=90.00%表5-7量具研究比较一相同的5个零件,有和无零件内变差(WIV)研究类型量具重复性变差再现性变差量具R&RWIV零件间变差总过程变差R&R占总过程变差%重复性单独占总变差%再现性单独占总变差%带WIV不带WIV0.05340.2000.1770.1780.1820.2690.18201.1441.1441.1781.17515.9%22.9%4.2%17.0%15.3%15.3%表5-8量具数据一览表零件12345基准值2.004.006.008.0010.002.705.105.807.609.102.503.905.707.709.302.404.205.907.809.502.505.005.907.709.30试52.703.806.007.809.402.303.906.107.809.50验72.503.906.007.809.502.503.906.107.709.50次92.403.906.407.809.602.404.006.307.509.20数112.604.106.007.609.302.403.806.107.709.40零件平均值2.494.136.037.719.38基准值2.004.006.008.0010.00偏倚+0.49+0.13+0.03-0.29-0.62极差0.41.30.70.30.5表5-9：计数型量具研究（小样法）A评价人B评价人12121GGGG2GGGG3NGGGG4NGNGNGNG5GGGG6GGGG7NGNGNGNG8NGNGGG9GGGG10GGGG11GGGG12GGGG13GNGGG14GGGG15GGGG16GGGG17GGGG18GGGG19GGGG20GGGG离散型数据测量系统分析测量原始记录表(3个测量者)零件号第一次测量结果第二次测量结果ABCABC100000020100003111111400000051011006111001711011080000009010001100101001111011012000000130000001400001015010110161011011700000018000001191011112011111121000000221110112300000024111110250000002611111127100100280000002911111130110011离散型数据测量系统分析重复性百分比处理记录表(3个测量者)零件号实际不一致次数第一次测量第二次测量ABCA1B1C1A2B2C2100000000020100100003000111111400000000050011011006110111001700011011080000000009001000001101000001001100011011012000000000130000000001401000001015100010110160001011011700000000018001000001190101011112001011110121000000000221001110112300000000024001111110250000000002600011111127000100100280000000002900011111130101110011合计不一致次数555不一致总次数15重复性百分比的计算检查员机会总次数实际不一致次数重复性百分比A30583.3%B30583.3%C30583.3%离散型数据测量系统分析再现性百分比处理记录表(3个测量者)样品号第一次测量第二次测量第一次测量不一致次数第二次测量不一致次数A1B1C1A2B2C2A1-B1A1-C1B1-C1A2-B2A2-C2B1-C2100000000000020100001010003111111000000400000000000051011001011106111001000011711011001101180000000000009000001000011100001000001101111011001101112000000000000130000000000001400001000010115010110101011161011011011011700000000000018000001000011191011111010002011110100010121000000000000221110110001002300000000000024111110000000250000000000112611111100000027100100110110280000000000002911111100000030110011011110合计不一致次数64881210不一致总次数48%再现性=100*实际一致的总次数/机会总次数(对所有操作者分次单独比较)N´为偶数:机会总次数=零件数n*(每个零件每次被测量的机会数N´2/4)N´为奇数:机会总次数=零件数n*[(每个零件每次被测量的机会数N´2-1)/4]实际一致的总次数=机会总次数-实际不一致的总次数(所有操作者分次比较测量同一零件的测量结果之间的结果)离散型数据测量系统分析一致性百分比处理记录表(3个测量者)零件号不一样次数对比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一致性(%GR&R)=100*实际一致的总次数/可能一致的总次数(对所有操作者分次单独比较)=N´为偶数:可能一致的总次数=零件数n*(每个零件每次被测量的机会数N´2/4)N´为奇数:可能一致的总次数=零件数n*[(每个零件每次被测量的机会数N´2-1)/4]实际一致的总次数=可能一致的总次数-实际不一致的总次数(对所有零件各次测量结果分别比较不一致的次数之和)离散型数据测量系统分析与标准一致性百分比处理记录表(3个测量者)零件号测量次数测量结果标准与标准一致的测量次数ABCABC110000000200000002101000102000000031111100021111000410000000200000005110110102100101161111100020011110711100110211001108110000002000000091100000020010001101000000021000100111110100121101001121000000020000000131000000020000000141000000020100010151010110121101011161101101021011010171000000020000000181000000020010001续表零件号测量次数测量结果标准与标准一致的测量次数ABCABC191101101021111000201111100021011000211000000020000000221111100020111100231000000020000000241111100021101001251000000020000000261111100021111000271100010021000100281000000020000000291111100021111000301110100120111100与标准一致的测量次数合计514851%与标准一致性(测量的准确度)=与标准一致的测量次数(按操作者分别比较)/各操作者测量的总次数=各操作者测量的总次数=零件数n*各操作者对同一零件重复测量的次数=χ2分布的α分位数表dƒx20.005x20.01x20.025x20.05x20.10x20.90x20.95x20.975x20.99x20.99510.0000390.000160.000980.00390.01582.713.845.026.637.8820.01000.02010.05060.10260.21074.615.997.389.2110.6030.07170.1150.2160.3520.5846.257.819.3511.3412.8440.2070.2970.4840.7111.0647.789.4911.1413.2814.8650.4120.5540.8311.151.619.2411.0712.8315.0916.7560.6760.8721.241.642.2010.6412.5914.4516.8118.5570.9891.241.692.172.8312.0214.0716.0118.4820.2881.341.652.182.733.4913.3615.5117.5320.0921.9691.732.092.703.334.1714.6816.9219.0221.6723.59102.162.563.253.944.8715.9918.3120.4823.2125.19112.603.053.824.575.5817.2819.6821.9224.7326.76123.073.574.405.236.3018.5521.0323.3426.2228.30133.574.115.015.897.0419.8122.3624.7427.6929.82144.074.665.636.577.7921.0623.6826.1229.1431.32154.605.236.267.268.5522.3125.0027.4930.5832.80165.145.816.917.969.3123.5426.3028.8532.0034.27186.267.018.239.3910.8625.9928.8731.5334.8137.16207.438.269.5910.8512.4428.4131.4134.1737.5740.00249.8910.8612.4013.8515.6633.2036.4239.3642.9845.563013.7914.9516.7918.4920.6040.2643.7746.9850.8953.674020.71`22.1624.4326.529.0551.8155.7659.3463.6966.776035.5337.4840.4843.1946.4674.4079.0883.3088.3891.9512083.8586.9291.5795.70100.62140.23146.57152.21158.95163.64t分布的α分位数表dƒt0.60t0.70t0.80t0.90t0.95t0.975t0.99t0.99510.3250.7271.3763.0786.31412.70631.82163.65720.2890.6171.0611.8862.9204.3036.9659.92530.2770.5840.9781.6382.3533.1824.5415.84140.2710.5690.9411.5332.1322.7763.7474.60450.2670.5590.9201.4762.0152.5713.3654.03260.2650.5530.9061.4401.9432.4473.1433.70770.2630.5490.8961.4151.8952.3652.9983.49980.2620.5460.8891.3971.8602.3062.8963.35590.2610.5430.8831.3830.8332.2622.8213.250100.2600.5420.8971.3721.8122.2282.7643.169110.2600.5400.8761.3631.7962.2012.7183.106120.2590.5390.8731.3561.7822.1792.6813.055130.2590.5380.8701.3501.7712.1602.6503.012140.2580.5370.8681.3451.7612.1452.6242.977150.2580.5360.8661.3411.7532.1312.6022.947160.2580.5350.8651.3371.7462.1202.5832.921170.2570.5340.8631.3331.7402.1102.5672.898180.2570.5340.8621.3301.7342.1012.5522.878190.2570.5330.8611.3281.7292.0932.5392.861200.2570.5330.8601.3251.7252.0862.5282.861210.2570.5320.8591.3231.7212.0802.5182.831220.2560.5320.8581.3211.7172.0742.5082.819230.2560.5320.8581.3191.7142.0692.5002.807240.2560.5310.8571.3181.7112.0642.4922.797250.2560.5310.8561.3161.7082.0602.4852.787260.2560.5310.8561.3151.7062.0562.4792.779270.2560.5310.8551.3141.7032.0522.4732.771280.2560.5300.8551.3131.7012.0482.4672.763290.2560.5300.8541.3111.6992.0452.4622.756300.2560.5300.8541.3101.6972.0422.4572.750400.2550.5290.8511.3031.6842.0212.4232.704600.2540.5270.8481.2961.6712.0002.3902.6601200.2540.5260.8451.2891.6581.9802.3582.617∞0.2530.5240.8421.2821.6451.9602.3262.576F分布的0.95分位数F0.95(n1,n2)表n1n21234567891012152024304060120∞1161.4199.5215.7224.6230.2234.0236.8238.9240.5241.9243.9245.9248.0249.1250.1251.1252.2253.3254.3218.5119.0019.1619.2519.3019.3319.3519.3719.3819.4019.4119.4319.4519.4519.4619.4719.4819.4919.50310.139.559.289.129.018.948.898.858.818.798.748.708.668.648.628.598.578.558.5347.716.946.596.396.266.166.096.046.005.965.915.565.805.775.755.725.695.665.6356.615.795.415.195.054.954.884.824.774.744.684.624.564.534.504.464.434.404.3665.995.144.764.534.394.284.214.154.104.064.003.943.873.843.813.773.743.703.6775.594.744.354.123.973.873.793.733.683.643.573.513.443.413.383.343.303.273.2385.324.464.073.843.693.583.503.443.393.353.283.223.153.123.083.043.012.972.9395.124.263.863.633.483.373.293.233.183.143.073.012.942.902.862.832.792.752.71104.964.103.713.483.333.223.143.073.022.982.912.852.772.742.702.662.622.582.54114.843.983.593.363.203.093.012.952.902.852.792.722.652.612.572.532.492.452.40124.753.893.493.263.113.002.912.852.802.752.692.622.542.512.472.432.382.342.30134.673.813.413.183.032.922.832.772.712.672.602.532.462.422.382.342.302.252.21144.603.743.343.112.962.852.762.702.652.602.532.462.392.352.312.272.222.182.13154.543.683.293.062.902.792.712.642.592.542.482.402.332.292.252.202.162.112.07164.493.633.243.012.852.742.662.592.542.492.422.352.282.242.192.152.112.062.01174.453.593.202.962.812.702.612.552.492.452.382.312.232.192.152.102.062.011.96184.413.553.162.932.772.662.582.512.462.412.342.272.192.152.112.062.021.971.92194.383.523.132.902.742.632.542.482.422.382.312.232.162.112.072.031.981.931.88204.353.493.102.872.712.602.512.452.392.352.282.202.122.082.041.991.951.901.84214.323.473.072.842.682.572.492.422.372.322.252.182.102.052.011.961.921.871.81224.303.443.052.822.662.552.462.402.342.302.232.152.072.031.981.941.891.841.78234.283.423.032.802.642.532.442.372.322.272.202.132.052.011.961.911.861.811.76244.263.403.012.782.622.512.422.362.302.252.182.112.031.981.941.891.841.791.73254.243.392.992.762.602.492.402.342.282.242.162.092.011.961.921.871.821.771.71264.233.372.982.742.592.472.392.322.272.222.152.071.991.951.901.851.801.751.69274.213.352.962.732.572.462.372.312.252.202.132.061.971.931.881.841.791.731.67284.203.342.952.712.562.452.362.292.242.192.122.041.961.911.871.821.771.711.65294.183.332.932.702.552.432.352.282.222.182.102.031.941.901.851.811.751.701.64304.173.322.922.692.532.422.332.272.212.162.092.011.931.891.841.791.741.681.62404.083.23.2.842.612.452.342.252.182.122.082.001.921.841.791.741.691.641.581.51604.003.152.762.532.372.252.172.102.041.991.921.841.751.701.651.591.531.471.391203.923.072.682.452.292.172.092.021.961.911.831.751.661.611.551.501.431.351.25∞3.843.002.602.372.212.102.011.941.881.831.751.671.571.521.461.391.321.221.00相关系数