GB 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

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

Statisticalinterpretationofdata

One-sidedreliabilityconfidencelowerlimit

(Binomialdistribution)

1引言

1.1本标准所用统计学名词见GB8358-82《统计学名iaij及符号》，可靠性名i,,l见GB3187一82

《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卜限Yit卜也可用J一可化

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}个个体作为样本.本标准规定J’从J-

这类样本确定产品可靠度单侧置信F限的方法。

1.3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一q

_0.1时，。次抽取可以认为是独立的。

1.‘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

对样木大小n，失败数F，在置信水平，F，可靠度R的单侧置信下限R,,按以卜公式if算:

F二0，R,-="vi一Y············，············『··，··⋯(1)

尸一“，n(n)R-'x“一凡，’=，一:····················一(2’

F二”一1，R,,二”v节，·、，······················一(3)

F二n，R二0

对试验结果n,F及指定的Y,产品可靠度R不小卜对应的表列值凡_的概率不低少，，即

P;R夕RL}夕:

1.4.2数表的参数范围与表距:

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

”二1(1)70(5)100(10)140(20)200(50)1000

F二0(1)20

1.5本标准所列数表未给出的{L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。

1.6L`vN9}i:例

国家标准局1985012，发布19851001实施

GB4087.8-85

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，求可靠度单侧置信哪民。

相应于。二10o,F二1，V=0.90查表得

刀[二0.96166

例2:

某电f-lx备使用寿命服从指数分布，其任务时ialto=250/J、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A..

根据指数分布可靠性估计理论有:

R,_e-".

因此

几u

相1,-,iI`n=80,F=2，v二o.9oiti.}得

六‘·

R,=0.93484

In

小

2500.93484

二0.00026952

GB4087.8-85

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94387

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.95170

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89060

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79955

81353

82568

.67620

.70242

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50000

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41189

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.89730

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84578

.85419

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96753

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97031

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92136

92488

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87469

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.83561

.84266

84912

.85508

.78109

.79089

.79985

.80808

.81565

.73426

74616

.75703

.76701

.77621

.68742

.70141

.71420

.72594

.73676

.97369

.97465

.97555

.97638

.97716

.93628

.93861

.94078

.94280

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.90219

90564

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91186

82265

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83517

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79990

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74675

75602

76463

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97789

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94645

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96528

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94229

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85910

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