One-sided reliability confidence lower limit (Normal distribution complete sample)

The statistical terms and symbols used in this standard are referred to GB 2258-82 "Statistical Terms and Symbols", and the reliability terms are referred to GB 3187-82 "Basic Terms and Definitions of Reliability". GB 4885-1985 Normal Distribution Complete Sample Reliability One-Sided Confidence Lower Limit GB4885-1985 Standard Download Decompression Password: www.bzxz.net
The statistical terms and symbols used in this standard are referred to GB 2258-82 "Statistical Terms and Symbols", and the reliability terms are referred to GB 3187-82 "Basic Terms and Definitions of Reliability".

1 Introduction
National Standard of the People's Republic of China
One-sided reliability confidence lower llmlt(Normat distribution complete sample)UDC 519.28
GB 4885-85
1.1 The statistical terms and symbols used in this standard can be found in GB3358-82 "Statistical Terms and Symbols", and the reliability terms can be found in GB3187-82 "Basic Terms and Definitions of Reliability". 1.2 This standard is applicable to the case where the product characteristic value X can be reasonably considered to obey the normal distribution. Its distribution density function is f(r)=
aV2元exp [
Formula μ is the population expected value and is the population standard deviation. ()\, 18+8
1.3 This standard is based on the product characteristic value X from the same population of sample size n independent random sample a1,2, medicine and given
a certain confidence level, when μ, unknown, for a given characteristic value upper (or lower) limit for the given method to determine the reliability of the one-sided confidence lower limit R.
2 Determination of reliability one-sided confidence lower limit
This standard provides two methods to determine the reliability lower limit, the table method and the direct method. The table method is simple and easy, but the accuracy is low. The direct method should be used in situations where higher accuracy is required. 2.1 Table method
2.1.! Calculate the sample mean and sample standard deviation s from the sample observation values ​​1, 2, ., n: (; -)2
2.1.2 Calculate the coefficient K according to the upper (lower) limit of the characteristic value: When the upper limit U is specified, =-
When the lower limit L is specified, K:
2.1.3 From the given confidence level, sample size n and the calculated K value, refer to the K coefficient table in Appendix A of this standard to obtain the reliability lower limit RL of the characteristic value X issued by the National Bureau of Standards on January 29, 1985
Implementation on October 1, 1985
GB4885—85
2.1.4*Example
A pressure vessel is subjected to internal pressure, and its compressive strength obeys the normal distribution. The failure stress of the container in 10 static tests is 2565, 2960, 2685, 2755, 2790, 2720, 2634, 2860, 2905, 2825 kg/cm2. The lower limit of the container compressive strength is 1.=2200 kg/cm2. Given the confidence level y=0.90, it is required to estimate the one-sided lower confidence limit of the reliability of the container. According to the 10 test data of the failure stress, the sample mean and sample standard deviation s are calculated: =2769.9, s=123.1
2769.9-2200
According to =0.90, n=10, K=4.6300, the K coefficient table in Appendix A is obtained: R,= 0.9990
That is, the one-sided confidence lower limit of the reliability of the container under the confidence level =0.90 is 0.9990. 2.2 Direct method
2.2.1 Solve the nonlinear equation
nX +nhu)
XL. In the formula,
「-U, when the upper limit of the characteristic value is given,
（L-, when the lower limit of the characteristic value is given,
in (·) standard normal distribution function
r(\=l)
——gamma function with parameter —
2.2.2 Calculation of one-sided lower confidence limit of reliability RLR=Φ（)
Appendix B (reference) of this standard gives a computer program for the direct method. 36
(n-1)s*h dh = 1 -y .(1)
GB 4885—85
K coefficient table for determining the one-sided confidence lower limit of the reliability of the normal distribution (supplement)
The parameter range and table interval of this coefficient table are:
=0.01,0.05,0.10,0.20,0.40(0.10)0.90,0.95,0.99R=0.50,0.60(0.05)0.95,0.99,0.925,0.93,0.935,0.9,0.945,0.95,0.96,0.9n=2(1)50(10)120
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