GB/T 4087.3-1985 数据的统计处理和解释 二项分布可靠度单侧置信下限

UDC519.28

华人民共和国国家标丫隹

GB4087.3—85

数据的统计处理和解释

二项分布可靠度单侧置信下限

国家标准ㅤ可打印ㅤ可复制ㅤ无水印ㅤ高清原版ㅤ去除空白页

Statisticalinterpretationofdata

One-sidedreliabilityconfidencelowerlimit

(Binomialdistribution)

19850129发布198510-01实施

圍标准局批准

中华人民共和国国家标准

UDC519.28

数据的统计处理和解释

二项分布可靠度单侧置信下限GB4087.3—85

Statisticalinterpr'etationofdata

One-sidedreliabilityconfidencelowerlimit

(Binomialdistribution)

1引言

1.1本标准所用统计学名词见GB3358-82《统计学名词及符号》，可靠性名词见GB3187-82

《可靠性基本名词术语及定义》。

1.2本标准适用于产品试验结果为成功、失败两种状态的可靠度单侧置信下限估计，也可用于可化

为此种情形的其他场合。从产品总体中随机地、独立地抽取若于个个体作为样本，本标准规定了基于

这样本确定产品可靠度单侧置信下限的方法。

1.8对有限总体，设其大小为N,样本大小为“。当抽取是有放回时,或当抽取是无放回的，但n/N

<0.1时，n次抽取可以认为是独立的。

1.4本标准的主要内容以数表形式列出。

1.4.1数表的计算公式国家标准ㅤ可打印ㅤ可复制ㅤ无水印ㅤ高清原版ㅤ去除空白页

对样本大小71,失败数F,在置信水平y下,可靠度7的单侧置信下限Rl按以下公式#算：

F=0,Rl="y1-y(1)

f〉o,2(汀橙(1讥宀1(2)

F=n-A,=1-"y/y'(3)

F~n,7?l二0

对试验结果n、F及指定的y,产品可靠度R不小于对应的表列值Rl的概率不低于y,即

P{R>Rl}>y

1.4.2数表的参数范围与表距:

'7=0.50(0.10)0.90,0.95,0.99

n=1(1)70(5)100(10)140(20)200(50)1000

Fw0(1)20

1.5本标准所列数表未给出的Rl值可利用本标准提供的数据内插计算，也可按本标准附录a给出

的近似公式计算。

1.6应用示例/

国家标准局19850129发布198510-01实施

GB4087.3—85

例1：

某爆炸螺栓试验了100件，失败一件，规定置信水平为0.90,求可靠度单侧置信下限。

相应于n=100,F=1,y=0.90査表得

Rl=0.96166

例2:

某电子设备使用寿命服从指数分布，其任务时间/o=25O小时，今试验数"=80,失败数F=2

未记录失效时间，置信水平为0.90,求该设备失效率上限九。

根据指数分布可靠性估计理论有：

Rl=e'九“

因此

Au=—In

foRl

相应于n-80.,F=2,v=0.90查表得

&=0.93484

故

.九=---1n

2500.93484

=0.00026952

国家标准ㅤ可打印ㅤ可复制ㅤ无水印ㅤ高清原版ㅤ去除空白页

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