GB 11179-1989 橡胶试验数据分布类型检验规定.pdf 12页

'中华人民共和国国家标准GB11179一89橡胶试验数据分布类型检验规定Rubber-testrulefordistributiontypeoftestingdata1主肠内容和适用范围本标准规定了用j方法检验橡胶试验数据分布类型的基本程序。根据本标准可以确定产品质量指标和经济指标的分布类型，亦可确定橡胶或橡胶制品试验数据的分布类型。本标准适用于检验橡胶试验观测值、观测值进行函数变换后的数据及随机数据经验分布与理论分布类型的拟合度。2引用标准GB528硫化橡胶拉伸性能的测定GB3187可靠性基本名词术语及定义GB3358统计学名词及符号GB4882数据的统计处理和解释正态性检验3符号Ha—原假设;，—样本大小;X=X2,""",X,—样本的。个顺序统计量观测值;F(X;)—观测值为X，时，理论分布的函数值;a—检验的显著性水平;砖—检验所用的统计量;G(2)—w:值的分布函数。其数值见附录A,4应用条件4.1当怀疑样本来自某个已知的总体分布时，应进行相应分布类型的检验。4.2w"检验方法可用于各种分布的检验，抽样必须保证随机性，随机变量的观测值应在相同条件下取得。被观测的样本必须来自同一总体。4.3样本大小不得小于50,4.4当需要由样本估计众数、加权平均值或加权标准差时，必须把样本等距离分组，组数，取决于样本大小。r与样本大小。的关系是:n=5099r=1015n=100-199T二1518中华人民共和国化学工业部1989一03一10批准1990一01一Ol实施 GB11179一89n二200r=18^-20n=400r二25-30n=1000r=35405实施步骤5.1给出Ho:样本来自某个已知理论分布。5.2将观测值排列为顺序统计量X=Xz，一，X.5.3计算理论分布函数值F(X)一丁少(X,)dx····································⋯⋯川()=1,2,""",n)5.4按式(2)计算说:“-一2客22云2n1InF(X,)+(‘-21云2n1)InC‘一“(X,)D········⋯⋯(2，计算时按表1填满数据。表1中的中间结果计算到五位有效数字，最后结果保留三位有效数字。将表1第10列累加起来，按公式(2)计算得到6;.5.5在附录A中与w相应的分布函数值G(w:),5.6取显著性水平a=0.2,5.了作出判断:如果G(w,))l一。，则拒绝Hp，即拒绝经验分布与理论分布相符合的假设;如果G(Q)<1-a，则接受这种假设按扩检验正态分布的举例见附录B;BASIC程序见附录C. GB11179一89拭李裤卞划粼1稍 GB11179一89附录AG(o)!)值(补充件)表Al0.ol0.020.030.040.050.060.070.080.090.100.00.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.10.0oo0.0000.0000.0010.0010.0020.0030.0040.0060.0080.20.0110.0140.0180.0.0270.0320.0380.0440.0540幻5R0.30.0660.0730.0820.0990.1080.1180.1270.1370.1470.40.1570.1670.1770.1860.1980.2080.2190.2290.2390.2500.50.2600.2700.2800.291n.3n10.3110.3200.3300.3400.3500.60.3590.3680.3780.3870.3960.4050.4140.4220.4310.4390.70.4480.4560.4640.4720.4800.4880.4950.5030.5100.51190.80.5250.5320.5390.5460.5530.5590.5660.5720.5790.585亡0Jd.0.9叶通0.5970.6030.6090.6140.6200.6260.6310.6370.6426J月弓了0.0.6520.6570.6620.6670.6720.6770.61910.6860.690卜h0巧1.1甘0.6990.7030.70190.7120.7160.7200.7240.7280.7320.7350.7390.7430.7460.7500.7530.7570.7600.7640.7670.7700.7730.7760.7790.7820.7850.7880.7910.7940.7970.8000.8020.8050.8080.8100.8130.8150.8180.8200.8231.50.8250.8270.8300.7320.8340.8360.8390.8410.8430.A450.8470.8490.8510.8530.8550.8570.8590.8600.8620.9640.9660.8670.8690.8710.R730.8740.8760.8770.8790.8800.8920.8840.8850.8860.8890.8890.8910.8920.8930.吕950.8960.8970.R990.9000.9010.9020.9040.9050.9060.9072.00.9090.9100.9110.9120.9130.9140.9150.9160.9170.9190.9190.9200.9210.9220.9230.9240.9250.9260.9270.92820.9280.9290.93009320.9330.9330.9340.9350.936川0.9370.9370.93R0.9400.9400.9410.9420.9420.943望0.9440.9440.9450.9460.9460.9470.9480.94R0.9490.949训 GB11179一89续表Al0.010.020.030.040.050.060.070.080.090.102.50.9500.9510.9510.9520.9520.9530.9530.9540.9550.9552.60.9560.9560.9570.9570.9580.9580.9590.9590.9600.9602.70.9600.9610.9610.9620.9620.9620.9630.9630.9640.9642.80.9650.9650.9660.9660.9660.9670.9670.9670.9680.9682.90.9690.9690.9690.9700.970附录B示例(参考件)选用天然橡胶硫化胶试样，按GB528的4号裁刀得到一个:=57的拉伸强度(单位:MPa)的样本。用护方法检验总体是否服从正态分布。BI给出Ha:样本来自正态分布。B2将观测值排列为顺序统计量(见表B1),B3按观测数据计算正态分布的参数估计量X"s和所有的理论分布函数值:}L57I:jX一j=517-一‘6.689·...·⋯⋯。。·。。··................(BI)7(X;一X)2Sz=一七」=1.2627.................................(B2)56S=1.1237F(Xj)一冬I‘Je卫y3=dx....................................(B3)丫2as,-m(j=1,2，一，57)分别把顺序统计量序号，和顺序统计量X，的理论分布值F(Xj)填人表I的第1列和第3列，再按表1的第2列及第4至10列各计算式计算，填入对应结果构成表B2，其中的第10列数值相加得一28.715嵘二一57一2X(一28.715)=0.430B4给出显著性水平a=0.2B5查附录A得O(o;)=a(0.43)=0.1771一“=0.8c(时)G1一a接受Ho:原样本来自正态分布的总体。 GB11179一89表BI排成顺序统计量的原始数据{:.:14.414.915.315.415.615.7]5.916.016.0::.:16.316.516.5::.:16.616.R16.8::.:::.;17.217.4::.:17.7::.:::.:::.:17.8{:.;::.:17.918.018.118.618.618.7表B2用表B1的数据按表1中各计算式计算所得结果~一~一~.-.-.一一，一.-，一目一种~一一，一‘一-明一一l23一6一一0一一~一~一.~一一一0.0026090.00299一5.81199一0.050980.991230.99701一0.00300一0.00297一0.053950410.00653一5.03087一0.132390.973680.99347一0.00655一0.00638一0.138770610.02081一3.87246一0.169840.956140.97919一0.02103一0.02010一0.189950.05561一2.88944一0.177420.938600.94439一0.05721一0.05370一0.2311250.0790.06631一2.71339一0.214220.921050.93369一0.06861一0.06320一0.277410.0960.10803一2.22536一0.214730.903510.89197一0.11432一0.10329一0.3180270.1140.12545一2.07584一0.236720.885960.87455一0.13405一0.11876一0.3554880.10149320.16594一1.79611236330.868420.8340618145一0.15758一0.393919二:0.1890566574248400.850880.81095二2095517830一0.4267010016701810.21404二54159一0.256930.833330.78596一0.24085二:20071一0.457641一0.2408542357一0.262240.815790.75915一0.27556一0.22480一0.4870412J0.2020.24085一42357一0.287210.798250.75915一0.27556一0.21996一0.5071813-0.2190.2408542357一0.312190.780700.75915一0.27556一0.21513一0.52732州一0.2370.2694031157310640.763160.73060一0.31388一0.23954一0.55018]5一0.2540.2694031157二:333650.745610.73060一0.31388一0.23404一0.5676816-0.2720.2694031157一0.356660.728070.73060一0.31388一0.22853一0.58519170.夕Rg0.26940一31157一0.379670.710530.73060一0.31388一0.22302一0.60269180.33113一1.10525一0.339330.692980.66887一0.40216一0.27869一0.6180219::::0.36396一1.01070一0.328030.675440.63604一0.45250一0.30564一0.6336720-0.3420.3639601070一0.345770.657890.63604一0.45250一0.29770一0.6434621一0.3600.36396一0.363500.640350.63604一0.45250一0.28976一0.653262一0.3770.36396:::::一0.381230.622810.63604一0.45250一0.28182一0.66305胎们3950.43249一0.83820一0.330870.605260.56751一0.56650一0.34288一0.67375别0.43249一0.83820一0.345570.587720.56751一0.56650一0.33294一0.67851肠:.:;;0.43249一0.83820一0.360280.570180.56751一0.56650一0.32300一0.69628筋0.4470.4676775999一0.339990.552630.53233一0.63050348430.68843所0.4650.46767二:75999一0.353330.535090.53233一0.63050二:337370.69070朋0.4RZ0.46767一0.75999一0.366660.517540.53733一0.63050一0.32631一0.59297别Ift GB11179--89续表B2-一一一一一一12345678910-一~一一.----一一~-一-~一--一--.~.一一--一-290.5000.50311一0.68694一0.343470.500000.49689一0.699390.349700.69317劝0.53853一0.61892一0.320320.482.460.46148一0.773330.37310一0.69:34."?31::;:0.53853一0.61892331180.464910.46148一0.77333一0.359530.69071能0.53853一0.61892二:342040.447370.46148一0.773330.34596一D.688003:.:::0.57364一0.55576一0.316880.429820.42636一0.85246一0.366416832934刊0.57364一0.55576一0.32.663D.412朴280.42636一0.35145_:6780935:.:::-10.64188一0.44336一0.2683500.358120.405350.6737036朴0.6230.67451一0.39177一0.2452400.32549一0.42337一0.66861盯朴0.6400.67451一0.39377一0.2.521500.32549二一一0.403680.65583380.6580.67451一0.39377一0.259060.342110.32549一一0.383990.6430539一0.6750.70586一0.34834一0.235290.324560.29414一0.39716一0.63245和一︵U︸0.6930.73573一0.306890.307020.26427一0.4085762125们八八一︺一U:一:;一二:0.7110.76398269220.289470.23062一0.417956092442八八一U一1-0.7280.7904923512171180.271930.20952一0.425010.5961943C204一州一0.7460.8151440一0.152400.254390.18486一0.429440.581844如一0.7630.81514一040一0.155990.236840.18486一0.399830.5558145月0.7810.81514一0.20440一0.159570.219300.184860.37021一0.52978妈月0.8151420440一0.163160.201750.19486一0.34059一()5037547二::.:一:0.8379117684一0.144260.184210.16209一1一0.335190.47946480.8330.83791一0.17684一0.147370.166670.16209一10.303270.45064钧0.8510.85879一0.15225一0.129540.149120.14122一1一0.291890.47141叨0.8680.85878一0.15225一0.132210.131580.14122一1一0.25755-038977别0.RR60.85878一0.15225一0.134890.114040.14122一1一0.223ZI35810520.9040.85878一0.15225一0.137560.096490.14122一1.95741一0.18887一0、32643岛0.9210.877740.13041一0.120110.078950.12226一210160一0.165920.28603540.9390.8948411、11104290.061400.10516一225226一0.13830-0.24259肠0.9560.95518二个04586二:043850.043860.04482一310506一0.136190.181103560.9740.95518一0.04586一0.044650.026320.04482一3。10506一0.081710.12f,365?0.03703一3.29593一0.02891-0.066320.9910.96297一0.03774一0.037410.00877注:对正态分布检验，除用本方法外，亦可采用c64882附录C扩检验的BASIC程序(参考件)本程序用扩方法检验样本的正态分布与双重指数分布，1480.1490语句是留作添’上事其他分布II GB11179一89算语句的位置。此外，本程序以人机对话式输入分组后给出直方图。原始数据是以TXT为后缀的顺序文件给出的。附录A中的待查数据也是一个数据文件，并命名为A,DA,程序能自动查出对应的表值，当所查数据超出表中的范围时，程序可自动算出该值并打印出来。1八卫UWIDTHLPRINT1320CU户CLS;PRINTTAB(20)“数据分布类型检验总菜单”n八jUPRINTTAB(20)“jOqPRINT亡nJPRINTTAB(5)"1输入原始数据，，;;PRINTTAB(46)"2.构成顺序统计量”六六0IjPRINTTAB(5)"3.打印直方图”;1n1PRINTTAB(46)"4..2检验”;;PRINTTAB(5)"5.结束”0八0IPRINT";PRINT“”0C介UINPUT“请选择编号执行对应操作”,BH100ONBHGOSUB120,250,310,710,1600110GOTO20120CLS:INPUT“输人数据个数",K,INPUT“输入TXT文件名”,Q$130DIMX(K),A(K,11),;OPEN"C;"+Q$+".TXT"FORINPUTAS1140FOR1二1TOK;INPUT#1,X(I),NEXTI,CLOSE#1150XBA=0,SIGMA=0160FORI=1TOK170XBA=XBA+X(I)180NEXTI190XBA=XBA/K200FOR1=1TOK210SIGMA=SIGMA+(X(1)-XBA)-(X(I)-XBA)220NEXTI230SIGMA=SQR(SIGMA/(K-1))240RETURN250CI,S:PRINT“正在排序”260FORKK=1TOK-1270FORNN二1TOK一1280IFX(NN))X(NN十1)THENSWAPX(NN),X(NN+1)290NEXTNN,KK300RETURN310CLS:INPUT“输入分组个数，",R,H#=(X(K)-X(1))/R320NH=1000330IFQl$二"Y"ORBH=3THENERASES,ZZ340DIMS(R),ZZ(R)350FORRR=1TOR360S(RR)=0370ZZ(RR)二X(1)+(RR-0.5)-H-380NEXTRR390FORKK二1TOK400FORRR=ITOR61以 GB11179一89410IFX(KK)(=X(1)+RR.H#十0.001ANDX(Kx))=X(1)+(RR一1).H#一0.001THEN420ELSE440420S(RR)=S(RR)+1430GOTO450440NEXTRR450MEXTKK460F=S(1)470FORRR=1TOR480IFS(RR))=FTHEN490EISE510490F=S(RR)500R1=RR510NEXTRR520MO=X(1)(Rl一1)，H#+H#，(S(Rl)-S(R1一1))八2rS(R7)-S(R1一I)-S(Rl+l))530MZ=X(1)+(R-0.5)*H#540MZZ=2.5j(MZ-MO550FORRR=1TOR560PRINTUSING“#it##‘###";X(1)+(RR一1)-H#;;PRINT“一一一，，;二PRINTUSING“####.###";X(1)+RR.H#;;PRINTUSING“###”;570IFS(RR)()0THEN580ELSEPRINTUSING“#####.####";ZZ(RR);GOTO630580PRINTUSING“#####.####";ZZ(RR);590FORNN=ITOS(RR)600PRINTTAB(40+2，(NN-1));".";610IFNN=S(RR)THENPRINT“620NEXTNN630NEXTRR640INPUT“打印这幅直方图吗?Y/N",Q3$650IFQ3$="y"THENQ3$一“Y=660IFQ3$="Y"THENGOSUB1500670INPUT“重新分组吗?Y/N",QI$680IFQl$="y"THENQ1$二“Y"690IFQl$=""THEN310700Q1$="Y";RETURN710CI.S720PRINT“使用0法检验橡胶物理试验数据的分布类型是普遍有效的，这里仅给出正态分布与双重指数分布检验，并在1380-1400处留有检验其它分布类型的接口”730PRINT"740PRINT"1正态分布”750PRINT"2双重指数分布”760PRINT"3其它分布”770PRINT"4检验结束”780PRINT“";INPUT"请按序号选择，",BH2790IFBH2=4THEN1600‘子干干 GB11179一89800FORI=ITOK810A(1,I)二I:A(I,2)=(2.1一1)/(2-K)820ONBH2GOSUB1350,1450,1480,1600830A(1,3)二A):A(i,4)=LOG(A(1,3)):A(1,5)二A(1,2)-A(1,4):A(1.6)=1一A(1,2)840A(1,7)二1一A(I,3):A(1,8)二LOG(A(1,7)):A(I,9)二A(I,6)-A(I,8):A(1,10)=A(I,5)十A(1,9):A(I,I)二X(1)850NEXTI860SUM=O870FOMM二ITOK880SUM二SUM+AM，10)890NEXTM900OMEGA二INT((一K一2.SUM+0.005)-100/100!910FOR1二ITOK920PRINTUSING“###";A(1,1);;PRINTUSING“#徉###”;:A(1,2);930PRINTUSING“##.#####";A(I,3);:PRINTUSING“###.#####";A(1,4);940PRINTUSING“###.#####";A(1,5);:PRINTUSING“##.#####";A(1,5);950PRINTUSING“材井壮.#廿廿井材";A(1,7);:PRINTUSING“材###牡#廿#”;A(1,8);960PRINTUSING“########";A(1,9);:PRINTUSING“###.#####”;八(1,10);970NEXT1980LPRINT"."=";:LPRINTUSING“廿廿#，抹徉";OMEGA;990CODE%=100+OMEGA1000IFCODE?/,)295THEN1010ELSE12601010SS-01020FORJJ=0TO61030IFii二0THENAI二1:GOTO11301040IFJJ二ITHENA1=0.5:GOTO11301050FZ二JJ一0.51060FM=JJ1070A1一FZ/FM1080FORll=JJTHEN2STEP一11090FZ==FZ一1】100FM=FM一1]I10A1-At+FZ/FM1120NEXT11BI=(一l)一ii.(4-JJ十I)}EXP((一9.87202324#*(4-JJ+1)/(8，OMEGA)))11301140IFABS(BO(IF,一09THEN1310DBFFNPL(Y)一EXP(OMEGA/(8，(Y二Y十]))一((4‘11+1)‘3.1415926#二Y)2/(8】】50()MEGA))1160=10001170H=500/N曰只05=0.5*(FNPL(0)一FNPL(1000)) GB11179一891190FORL=1TON1200S=S+2*FNPL((2*L-1)*H)+FNPL(2*L"H)1210NEXTL1220C1=1000"S*2.506628/(3*N*OMEGA)1230SS=SS+Al*BI*Cl1240NEXTJJ1250GOTO13101260OPEN"A;DA"AS#2LEM=241270FIELD#2,8ASN$,8ASA$1280GET#2,CODE环1290SS=VAL(A$)1300CLOSE1310LPRINT"G(.2)=";;LPRINTUSING“#，###";SS1320INPUT“还作m2检验吗?Y/N",Q2$1330IFQ2$="y"THENQ2$=..Y=1340IFQ2$="Y"THEN710ELSERETURN1350B=(X(I)-XBA)/SIGMA1360C=一61370NI一501380H二(B-C/(2-N1)1390S=o.5，(EXP(-C"2/2))一(EXP(-B一2/2))/2.5066282#1400FORL=1TONl1410S=S+2，EXP(一(C+(2，L一1)，H)一2/2)/2.5066282#+EXP(一(C+2，L*H)一2/2)/2.5066282#1420NEXTL1430A1=(B-C>S/(3-N1)1440RETURN1450B=一EXP(MZZ8(X(I)-MO))1460Al二I一EXP(B);IFAl二1THENA1=0.999991470RETURN1480REMAl一待检验的某种分布的概率值1490REMRETURN1500FORRR=1TOR1510LPRINTUSING“####.##廿”;X(1)+(RR一1)*H#;:LPRINT“一一一，’;:LPRINTUSING“####.###";X(1)+RR*H#;.LPRINTUSING“###”;1520IFS(RR)(>0THEN1530ELSELPRINTUSING“#####.####";ZZ(RR),GOTO15801530LPRTNTUSING“#####.####";ZZ(RR);1540FORNN=1TOS(RR)1550LPRINTTAB(40+2，(NN一1));“.，，;1560IFNN=S(RR)THENLPRINT“”1570NEXTNN1590NFXTRR GB11179一891590RETURN1600END附加说明:本标准由全国橡胶与橡胶制品标准化技术委员会归口。本标准由化学工业部沈阳橡胶工业制品研究所起草。本标准主要起草人张信斌、舒静如。本标准参照采用苏联国家标准1"OCT11.006-79((经验分布与理论分布拟合度检验规则》。'