Standard ICS number:Sociology, Services, Organization and management of companies (enterprises), Administration, Transport>>Quality>>03.120.30 Application of statistical methods
Standard Classification Number:Comprehensive>>Basic Subjects>>A41 Mathematics
This standard specifies the method for determining the upper confidence limit of the coefficient of variation according to the confidence level given by the sample when the product characteristic value χ follows the normal distribution, the mean (μ>0) and the standard deviation δ are unknown. This standard is widely applicable to the estimation of the coefficient of variation of structures, materials, textiles, etc. GB/T 11791-1989 Upper confidence limit of the coefficient of variation of normal distribution GB/T11791-1989 Standard download decompression password: www.bzxz.net
This standard specifies the method for determining the upper confidence limit of the coefficient of variation according to the confidence level given by the sample when the product characteristic value χ follows the normal distribution, the mean (μ>0) and the standard deviation δ are unknown. This standard is widely applicable to the estimation of the coefficient of variation of structures, materials, textiles, etc.
Some standard content:
National Standard of the People's Republic of China Upper confidence limits of coefficientof variation for normal distribution Upper confidence limits of coefficientof variation for normal distribution1 Subject content and scope of application GB/T 11791---89 This standard specifies the method for determining the upper confidence limit of coefficient of variation based on the sample and a given confidence level when the product characteristic values obey the normal distribution, the mean (u0) and the standard deviation (u1) are unknown. This standard is widely applicable to the estimation of coefficient of variation of structures, materials, textiles, etc. 2 Referenced standards GB3358 Statistical terms and symbols GB318 Basic terms and definitions of reliability 3 Symbols Sample size Characteristic value of the t-th individual in the sample Sample mean Sample variance Sample coefficient of variation Coefficient of variation of the population Population Reciprocal of the coefficient of variation Confidence lower limit of C Distribution with (n-1) degrees of freedom Confidence level of -1-α quantile of ×2 distribution with (n-1) degrees of freedom 1-α quantile of non-central "t" distribution with (n-1) degrees of freedom and non-central parameter Confidence upper limit of the population coefficient of variation Estimation formula of the coefficient of variation Assume that the sample,…, comes from a normal population N (,), approved by the State Administration of Technical Supervision on November 22, 1989 326 Cya/μ x2(n-1) xi-,(n-1) tj-n(n- l;d) 1990·07-01 implementation GB/T 11791- 89 (—)2 When the confidence level is 1-α, u>0, the classical exact upper confidence limit Cvu of the overall coefficient of variation is determined by the following formula; [ti--(nl;Vn(C-))VnK Wu Zhong: K1/s=1/cvs. 4.1 Lookup table method Step 1: Calculate nk Step 2: According to the √n value, look up the tt (n;o) table in Appendix A (Supplement) of this standard and use linear interpolation to calculate the value, that is, ~/n (C\) Step 3: Calculate Cvu- 1/(Cv)L 4.2 Calculation method Step 1: Calculate √ element K Step 2: From the /nK value, calculate the value according to the calculation procedure of the non-central "t\ distribution (1-α) quantile provided in Appendix B (reference) of this standard, that is, the (C\) value. Step 3: Calculate Cvu = 1/(Cv)i 5 Approximate formula When C<0.30 and n=6, Cv is determined by the following approximate formula: Ciyu= 6 Example [ x-(n -- 1)(1 + Cs . (n= 1)- 1) C&s . (2) A batch of carbon epoxy shells, 9 pieces were randomly selected for strength test, and the measured damage values were (unit: t): 7.92.7.25, 7, 8.58, 7, 6.67, 6.75, 6.87, 6.92. Calculate the upper confidence limit of the coefficient of variation of the strength of this batch of shells when the confidence level is 0.90. Calculation: α-7. 217 8 (t) s== 0. 629 5 (t) (i) Approximate method . (8)-3.49, from (2) we get: Cvu =: 0. 131 6 (ii)Exact method From √nK34.3978, check the table in Appendix A and use linear interpolation: So we have yn (Cv)r = 22. 640 9 Gvu = 1/(Cv*) -The parameter range and table interval of this table are: 11791-89 Quantile table of non-central “t\ distribution (Supplement) 1α 0.70,0. 80,0. 90,0. 95,0. 99n=2(1)50,60,70,80 GB/T 11791--89 0821829 0816189 0982888 082798 8898989 01809889 02288269 021002 16 0880 089612 00620618 008 228 | | tt | | 010992 | |tt||016129 016869 0282202|| tt | t||0266292 0880289 r086892|| tt | 2896 00234502 GB/T11791-89|| tt||0880899 0862899 06266699 0086802 0086829 0078009 028889 07960899||tt| |029989 001889 0816009 0 196609 | | tt | |086665 091869 08890992||tt| |020919 818689 80333453339 GB/T11791-~ 0096692 009988 009008 005298 009629 008 691 000222 008282 0099 9282 | | tt | | 000298 | t||09196866 000829001 0000980.0m 0002961 000682 0008960 09989168 626086 0786628 08969606 02990026| |tt||03882686 002890101 00 9880100 000289801 982182 0188982 0296262 082891 09616128 998278 068228| |tt||069821 009822 00817 281 008698 0282867 C169196 00080262 0009886 008686 002161021 008900| |tt||006918 0016661 1002982 00601881 00892881 00091061 0066806 00029111 0068006 00680861 000616611|| tt||0090280 C08166801 00069880 086680 0089026 0088601 0088100 008101 000920-11 0962926 012826 09192626 02982626||tt| |09968086 02887186 06960286 0680118 03692286 0091886 09201686 00960066 399666 08210966 06898898 09906028 061118 09688728 122828 06266088 09699188 06920188 892698|| tt||03966988 08110888 08991 688 02628068 01881292 09829022 06821822 0282692 111622 099182 000192| |tt||0249982 33553880 GB/T 11791-89 080661 000816261 009896861 00911866 0021600 088602 0019899-81||tt ||0016281 002888881 0062266 00822668 001080% 0089600 000281 008198612||tt| |0097286 022188 G0f00G921 0028688 0091196 00206108 0002820 0089969 00059991 00000999 0028829| |tt||002982 0029922 02'0=0-1 00628882 ooftts 009859g 000169||tt ||0002081 0089158 009212 9 0060890 0069928 002896 000079 0009806 0009822 1179189 0092882| |tt||000828 0098968 009878961 000018 009061- 008628 000088 00028888|| tt||000916181 008296691 00 02869 002250 0020012 002191-2 0016812 008632 082828 019868 000009 0000980 0080960-91 00619019 0089191 006881 002681 000821 00969291 028128 089288 02:001 006198 008806 0099806 0019180 0062891 0068513 0021092 001669| |tt||0029682 0086018 0096298 088816 0066862 0069900t 0009290 0098620||tt ||8003234638304 GB/T 11791-- 009879 026689 00896992 090029 008909292 0069896 060222 000900622 000016 006262008 06299878 006215 008820 8 000880 009909692 009999 000618 0089288 0828012 009062092 00920199| |tt||001896 000829 001188898 0089610 00085902||tt ||0028891 0090682 0068609 0060218 0083680 009289 0060908 0099228 02°0-{ 002281 002092612 008281 002182 001888922 0020822 0069222 002022 000802 002218 0008626 009962 0022898|| tt||009809912 0092996 002629 000000 000992818 GB/T 11791-89 869892 002629 0000992 021189 0098662 230898189 009200652 029669 006199092 009612 000000 00902892 0000022 0059988 0099986|| tt||0088820 0092890 002809 00818292 000999 000282 002288 008882||tt| |00982682 000020 00268622 001867 00029892 0002092 0028892 00282822|| tt||00099622 000988 0022982 0096268 0218982 028282 000698 000200||tt| |002912 008606 000282 0088182 000898 0069000 0001811 0009908 0 22998wwW.bzxz.Net 0089168 008202 00020902 006663 021902 008002 00219102 001129| |tt||0060202 002189202 80832343333804 GB/T11791-89 00088927 061282 00 686828 009996 0008212 008982 00688628 0088888 0066021 00288928 0029288| |tt||00900818 001802818 006202 0009669 06900828 00681678 008822|| tt||009128 061285-0 008860018 006828 00216818 0000980 0026292 00969288|| tt||000800 008102828 00t80990m 00901962 00908962 009890662 00286662|| tt||0000000 001860218 000020 0021808 000088 0081888 008029 002668||tt| |0066208 0080888 0080186 002680 009096162 00919262 008296 00020086 2 00208000 00068800 006989818 0000160 00926691 00220281 0088896 000226| |tt||008298 000606 0088669-62 0028969 0001088 0091108 6790223456211791-89 869892 002629 0000992 021189 0098662 230898189 009200652 029669 006199092 009612 000000 00902892 0000022 0059988 0099986|| tt||0088820 0092890 002809 00818292 000999 000282 002288 008882||tt| |00982682 000020 00268622 001867 00029892 0002092 0028892 00282822|| tt||00099622 000988 0022982 0096268 0218982 028282 000698 000200||tt| |002912 008606 000282 0088182 000898 0069000 0001811 0009908 0 22998 0089168 008202 00020902 006663 021902 008002 00219102 001129| |tt||0060202 002189202 80832343333804 GB/T11791-89 00088927 061282 00 686828 009996 0008212 008982 00688628 0088888 0066021 00288928 0029288| |tt||00900818 001802818 006202 0009669 06900828 00681678 008822|| tt||009128 061285-0 008860018 006828 00216818 0000980 0026292 00969288|| tt||000800 008102828 00t80990m 00901962 00908962 009890662 00286662|| tt||0000000 001860218 000020 0021808 000088 0081888 008029 002668||tt| |0066208 0080888 0080186 002680 009096162 00919262 008296 00020086 2 00208000 00068800 006989818 0000160 00926691 00220281 0088896 000226| |tt||008298 000606 0088669-62 0028969 0001088 0091108 6790223456211791-89 869892 002629 0000992 021189 0098662 230898189 009200652 029669 006199092 009612 000000 00902892 0000022 0059988 0099986|| tt||0088820 0092890 002809 00818292 000999 000282 002288 008882||tt| |00982682 000020 00268622 001867 00029892 0002092 0028892 00282822|| tt||00099622 000988 0022982 0096268 0218982 028282 000698 000200||tt| |002912 008606 000282 0088182 000898 0069000 0001811 0009908 0 22998 0089168 008202 00020902 006663 021902 008002 00219102 001129| |tt||0060202 002189202 80832343333804 GB/T11791-89 00088927 061282 00 686828 009996 0008212 008982 00688628 0088888 0066021 00288928 0029288| |tt||00900818 001802818 006202 0009669 06900828 00681678 008822|| tt||009128 061285-0 008860018 006828 00216818 0000980 0026292 00969288|| tt||000800 008102828 00t80990m 00901962 00908962 009890662 00286662|| tt||0000000 001860218 000020 0021808 000088 0081888 008029 002668||tt| |0066208 0080888 0080186 002680 009096162 00919262 008296 00020086 2 00208000 00068800 006989818 0000160 00926691 00220281 0088896 000226| |tt||008298 000606 0088669-62 0028969 0001088 0091108 67902234562 Tip: This standard content only shows part of the intercepted content of the complete standard. 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