【国家标准(GB)】 正态分布完全样本可靠度单侧置信下限

1引言
中华人民共和国国家标准
正态分布完全样本可靠度单侧置信下限One - sided reliabllity confidence lower llmlt(Normat distribution complete sample)UDC 519.28
GB 4885-85
1.1本标准所用统计学名词及符号见GB3358一82《统计学名词及符号》，可靠性名词术语见国标GB3187—82《可靠性基本名词术语及定义》。1.2本标准适用于产品特性值X可合理地认为服从正态分布的情形。其分布密度函数为f(r)=
aV2元exp [
式μ为总体期望值，为总体标准差。()\，18+8
1.3本标准基」产品特性值X来自同一总体的样本大小为n的独立随机样本a1，2，药及给
定的置信水平，当μ，未知时，对于给定的特性值上（或下）限给出了确定可靠度单侧置信下限R的方法。
2可靠度单侧置信下限的确定
本标准给出两种确定可靠度下限的方法，查表法和直接法。奎表法简便易行，但精度较低。在精度要求较高的场合应采用直接法。2.1查表法
2.1.！由样本观察值1，2，.，n计算样本均值，样本标准差s：(; -)2
2.1.2据特性值上（下）限计算系数K：当规定上限U时，=-
当规定下限L时，K：
2.1.3由给定的置信水平，样本大小n及算得的K值，反本标准附录A的K系数表，即得特性国家标准局1985-01-29发布
1985-10-01实施
值X的可靠度单侧置信下限RL
GB4885—85
2.1.4*表示例
某压力容器承受内压，其抗压癌度服从正态分布。该种容器10次静力试验的破坏应力分别为：2565，2960，2685，2755，2790，2720，2634，2860，2905，2825kg/cm。容器抗压强度的下限规定为1.=2200kg/cm2。给定置信水半y=0.90，要求估让该容器可靠度单侧置信下限。根据破坏应力的10个试验数据计算样本均值和样本标准差s：=2769.9,s=123.1
2769.9-2200
根据=0.90，n=10，K=4.6300附录A的K系数表得：R,= 0.9990
即该容器在置信水乎=0.90之下的可靠度单侧置信下限为0.9990。2.2直接法
2.2.1求非线性方程
nX +nhu)
解XL。式中
「-U，给定特性值上限时
（L-，给定特性值下限时
中（·）标准正态分布函数
r(\=l)
——参数为—
的伽玛函数
2.2.2计算可靠度单侧置信下限RLR=Φ（)
本标准附录B（参考件）给出了直接法的一-种计算机程序。36
(n-1)s*h dh = 1 -y .(1)
GB 4885—85
确定正态分布可靠度单侧置信下限的K系数表（补充件）
本系数表的参数范围与表距：
=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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