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.

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
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GB/T 11791--
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GB/T 11791-89
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GB/T11791-89
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