用数理统计的方法处理试验数据的异常值

20054No.42005ElectricWire&Cable20058Aug.,2005(0,300231):,,,,,?,,,:;;;;;:TM206:A:167226901(2005)0420046203TreatmentofAbnormalTestDatabyMathematicalStatisticsZHANGLi2wei(TianjinNo.609CableCo.,Ltd.,Tianjin300231,,China)Abstract:Sometimes,anabnormaldatummaybeseeninasetoftestdataforwireandcable.Outwardly,theabnormaldatummaybemuchgreaterorsmallerthanthevalueofanyotherdatum.Shallwediscardthisabnormaldatuminthetreatmentoftestdata?Judgementbyinstinctlackstheoreticalground.Thispaperpresentsamethodtoidentifytheabnormaldatumbymathematicalstatistics.Examplesweregivenandcalculationsweremade.Keywords:Wireandcable;test;datatreatment;mathematicalstatistics;abnormalvalue;discard:2004210212:(1976-),,,.:63[300231].1,,,,,,,,,,,,?,,,,,=0.0595%,,,22.1(Grubbs):,yj(j=1,2,3,n),,y1y2yn,y1,yny1yn,ys,gjg(,n),,,n,,=0.05,()95%1g(0.05,n),(1)(5)1g(0.05,n)n345678910111213g1.151.461.671.821.942.032.112.182.232.292.33n1415161718192025304050g2.372.412.442.472.502.532.562.662.752.872.96y=nj=1yjn(1)s=1n-1nj=1(yj-y)2(2)|y1-y||yn-y|:yj=y1(3)|y1-y||yn-y|:yj=yn(4)gj=|yj-y|S(5)(1)(5),gi1g(0.05,n):gig(0.05,n),;gjg(0.05,n),yj,n-1,,,m,:,,,11.56,2.09,2.09,2.09,2.23,2.33,2.42,2.42,2.56,2.6610,,:y=10j=1yj10=2.245s=110-110j=1(yj-y)2=0.313:|y1-y|=0.685|y10-y|=0.415:yj=y1=1.56gj=|yj-y|s=0.6850.313=2.191g(0.05,10)=2.18,gjg(0.05,n),,y1=1.56y1=1.56,n-1=9,:y=9j=1yj9=2.321s=19-19j=1yj-y2=0.212:|y1-y|=0.231|y9-y|=0.339:yj=y9=2.66gj=|yj-y|s=0.3390.212=1.5991g(0.05,9)=2.11,gjg(0.05,9),y9=2.66,1.56,2.2(Dixon)xj(j=1,2,3,n),,x1x2xn,x1,xn,xsn,r2r(0.05,n)2r(0.05,n)n345678r0.9410.7650.6420.5600.5070.554n910111213-r0.5120.4770.5760.5460.521-3n7:r=xn-xn-1xn-x1r=x2-x1xn-x18n12:r=xn-xn-1xn-x2r=x2-x1xn-1-x1n13:r=xn-xn-2xn-x3r=x3-x1xn-2-x1rr2r(0.05,n):r(r)r(0.05,n),(),,;r(r)r(0.05,n),(),,21,:n=10r=xn-xn-1xn-x2=2.66-2.562.66-2.09=0.1754r=x2-x1xn-1-x1=2.09-1.562.56-1.56=0.532r(0.05,10)=0.477,:rr(0.05,n),1.56,,;rr(0.05,n),2.667420054No.42005ElectricWire&Cable20058Aug.,2005,,2.3t,,,(n-1)uis:s=n-1i=1(x-x)2(n-1)-1=n-1i=1u2in-23tt(0.05,n-2)p=1-=1-0.05=95%tv=n-23t(0.05,n-2)3tt(0.05,n-2)n12345t12.714.3033.1822.7762.571n678910t2.4472.3652.3062.2622.228:|xi-x|=|ug|t(0.05,n-2)s,;,,,s35.29,5.29,5.30,5.28,5.31,5.27,5.30,5.31,5.32,5.2810,t,:5.32,5.32:x=1n-1n-1i=1xi=110-110-1i=1xi=5.292s=n-1i=1(x-x)2(n-1)-1=n-1i=1u2in-2=1.3910-2=0.01393:t(0.05,n-2)=2.306|ug|=|xi-x|=|5.32-5.292|=0.028t(0.05,n-2)s=2.3060.0139=0.03205:|xi-x|=|ug|t(0.05,n-2)s5.32,,3,,,,,,,,,,,!!!8420054No.42005ElectricWire&Cable20058Aug.,2005