標準解讀

《GB/T 4885-1985 正態(tài)分布完全樣本可靠度單側(cè)置信下限》是一項國家標準,主要針對的是基于正態(tài)分布的數(shù)據(jù)集,在給定的置信水平下計算可靠度(即生存函數(shù)值)的單側(cè)置信下限。該標準適用于具有已知均值和方差或可估計這些參數(shù)的情況下的產(chǎn)品質(zhì)量控制、可靠性分析等領(lǐng)域。

在實際應(yīng)用中,當處理一批產(chǎn)品時,如果其壽命遵循正態(tài)分布,則可以通過本標準提供的方法來評估這批產(chǎn)品的最低預(yù)期性能水平。具體來說,它定義了一系列步驟和技術(shù),包括但不限于確定樣本大小、計算統(tǒng)計量以及查找相應(yīng)的臨界值表等,用以構(gòu)建出一個合理的區(qū)間估計,從而幫助決策者了解在特定置信水平下產(chǎn)品至少能夠達到的性能標準。


如需獲取更多詳盡信息,請直接參考下方經(jīng)官方授權(quán)發(fā)布的權(quán)威標準文檔。

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  • 被代替
  • 已被新標準代替,建議下載現(xiàn)行標準GB/T 4885-2009
  • 1985-01-29 頒布
  • 1985-10-01 實施
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GB 4885-1985 正態(tài)分布完全樣本可靠度單側(cè)置信下限-免費下載試讀頁

文檔簡介

中華人民共和國國家標準

UDC引9.28

正態(tài)分布完全樣本可靠度單側(cè)置信下限

GS4885一[1b

One一sidedreliabilityconfidencelowerlimit

(Normaldistributioncompletesample)

1引言

1.1本標準所用統(tǒng)計學名L及符號見GB3358-82《統(tǒng)計學名詞及符號》,可靠性名詞術(shù)語見國標

GB3187-82《可靠性墓本名詞術(shù)語及定義)))o

1.2本標準適用于產(chǎn)品特性值h可合理地認為服從正態(tài)分布的情形。其分布密度函數(shù)為

f(x)二甲二1_rexp

uV乙Jt

r1rx一u\2-)

l一二r、-一戶一一夕J,一。。久x久+‘.

Zu

式中拜為總體期望值,a為總體標準差。

1.3本標準基1'產(chǎn)品特性值X來自同一總體的樣本大小為,的獨立隨機樣本XIsx2,.....,X.及給

定的置信水、}

的方法。

,,當N,"未知時,對于給定的特性值上(或下)限給出了確定可靠度單側(cè)置信下限R,

2可靠度單側(cè)皿信下限的確定

本標準給出兩種確定可靠度下限的方法,查表法和直接法。查表法簡便易行,但精度較低。在精

度要求較高的場合應(yīng)采用直接法。

2.,查表法

2.1.1

2.1.2

2.1.3

由樣本觀察值x1,X2,??,x計算樣本均值x,樣本標準差:

x=告全:

‘孫件1.(二一x)2

V幾一1.刁

據(jù)特性值七(一卜)限計算系數(shù)K.

當規(guī)}Lh限U時,K=we.U-x.r

當規(guī)定下限L時,K

x一L

s

X

由給定的置信水平Y(jié),樣木大小。及算得的K值,反杏本標準附錄A的K系數(shù)表,即得特州

國家標準局1985-01-2,發(fā)布

1985一10一01實施

GB4885一85

泊x的可靠度單側(cè)置信卜限R,,。

2.1.4杏表,J<例

某壓力容器承受內(nèi)壓,其抗壓強度服從IF杰分布。該種容器10次旅力試驗的破壞應(yīng)少}分別為:2565,

2960,12685,2755,2790,2720,2634,2860,2905,2825kg/cm'a容器抗壓強度的下限規(guī)定為l=2200

kg/cm2。給定置信水平v二0.90,要求估計該容器可靠度單側(cè)置信下限。

根據(jù)破壞應(yīng)力的10個試驗數(shù)據(jù)計算樣本均值萬和樣本標準差,:

x二2769.9.s二123.1

K二x-蘭

2769.9一2200

二二一二:

123.1

4.6300

根據(jù)v=0.90,。二10,K=4.6300杏附錄A,},的K系數(shù)表得:

Ri--0.9990

即該容器在置信水、I'v=0.90之卜的可靠度單側(cè)置信下限為。.9990.

2.2直接法

2.2.1求非線性方程

cPW-nXi+Jn下

n-聲,“)了竺-,

v)—h

廠件掃

一專(·

I),:^dh二1一v··?(1)

解X,。式

v二

少(

些,

x,

給定特性值上限時

給定特性i&ir限時

卜-工

·)—標準正態(tài)分布函數(shù)

rtn子)一參數(shù)為

刀一I

的伽瑪函數(shù)

2.2.2計算可靠度單側(cè)置信下限RL

凡二0(XL)·········,······················?!ぁぁぁぁぁぁひ?2)

木標準附錄B(參考件)給出了直接法的一種計算機程序。

GB4885一85

附錄A

確定正態(tài)分布可靠度單側(cè)置信下限的K系數(shù)表

(補充件)

本系數(shù)農(nóng)的參數(shù)范圍與表距:

1`0-01-0.05,0.10,0.20,0.40(0.10)0.90,0.95,0.99

RL=0.50,0.60(0.05)0.95,0.99,0.9'5,0.9',0.9'5,0.9',0.9'5,0.9',0.9',0.9

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