可靠性與壽命抽樣檢驗(yàn)可靠性的概念失效（故障）：系統(tǒng)喪失規(guī)定功能；系統(tǒng)失效即壽命終止；用隨機(jī)變量X代表系統(tǒng)的壽命；X的分布函數(shù)為：可靠性則為：F(0)=0,

F(∞)=1R(0)=1,

R(∞)=0可靠性的表征平均壽命MTTF中位壽命眾數(shù)壽命條件可靠性與失效率考慮系統(tǒng)已經(jīng)正常運(yùn)行到時(shí)刻t，隨后繼續(xù)運(yùn)行時(shí)間⊿t的概率，用條件概率的定義：上述四個(gè)函數(shù)是等效的，只要確定一個(gè)，系統(tǒng)的可靠性就是可知的。產(chǎn)品失效的浴盆曲線通過壽命試驗(yàn)進(jìn)行接收抽樣與通過計(jì)數(shù)值或計(jì)量值的接收抽樣不同，有些產(chǎn)品要考察其使用壽命，可靠性，失效率等指標(biāo)。需要通過壽命試驗(yàn)來獲得對(duì)上述指標(biāo)的決策。壽命實(shí)驗(yàn)通常都是截尾的。1、壽命試驗(yàn)壽命試驗(yàn)：以產(chǎn)品的工作條件進(jìn)行試驗(yàn)。完全壽命試驗(yàn)：很少有可能進(jìn)行完全壽命試驗(yàn)截尾壽命試驗(yàn)(censoring)定時(shí)截尾壽命試驗(yàn)–

（ｎ，無，時(shí)）–

（ｎ，有，時(shí)）定數(shù)截尾壽命試驗(yàn)–

（ｎ，無，數(shù)）–

（ｎ，無，數(shù)）例：（ｎ，有，時(shí)）抽?。顐€(gè)產(chǎn)品進(jìn)行有替換定時(shí)截尾壽命試驗(yàn)，截至?xí)r間為ｔ０，到試驗(yàn)截至?xí)r，樣品的總試驗(yàn)時(shí)間為Ｓ(t0)=nt0,設(shè)有r個(gè)產(chǎn)品失效的時(shí)間為：t1≤t2≤…≤tr

≤t0這是一個(gè)順序統(tǒng)計(jì)量，其聯(lián)合密度分布為：似然函數(shù)為：經(jīng)過極大似然估計(jì)，得到θ和λ的估。2、基于可靠性的抽樣檢驗(yàn)通過可靠性檢驗(yàn)的指標(biāo)主要有失效率，平均壽命，可靠壽命(tR)等等；指數(shù)分布(常失效率)情況失效率的抽樣方案 通過定時(shí)截尾試驗(yàn)進(jìn)行指數(shù)分布：抽樣規(guī)則從一批產(chǎn)品中抽取n個(gè)進(jìn)行壽命試驗(yàn)，到事先規(guī)定的截止時(shí)間時(shí)停止試驗(yàn)，如在這段時(shí)間里有r個(gè)產(chǎn)品失效，則規(guī)定，當(dāng)：r≤c，當(dāng)r>c，所以，本容量n，合格數(shù)c，

t。作（

n,t,c）方案。接收概率一個(gè)產(chǎn)品在[0，t]內(nèi)失效的概率為F(t)=P{T≤t},不失效的概率為R(t)=1-F(t)因此，n個(gè)產(chǎn)品壽命試驗(yàn)時(shí)失效r個(gè)的概率為：所以上述方案的接收概率為：這一概率是失效率的函數(shù)，也即失效率抽樣方案的OC曲線。當(dāng)λ很小，λt也相當(dāng)小接收概率可化：當(dāng)n大但nλt不大分布用泊松分布近似，可得：?表示的分布密度函數(shù)抽樣方案的制定(α,β)原則上述方程中有三個(gè)參量要確定給定試驗(yàn)時(shí)間，滿足上式的抽樣方案即標(biāo)準(zhǔn)型失效率抽樣方案；同樣，也可確定合適的抽樣量n，確定試驗(yàn)時(shí)間和合格判定數(shù)。失效率的LFR抽樣方案LFR：Limit

Failure

Rate為保證使用方要求，僅控制β和λ，即在L（λ1）＝β的前提下，用盡可能少的抽樣量和試驗(yàn)時(shí)間，同時(shí)適當(dāng)照顧生產(chǎn)方的風(fēng)險(xiǎn)。類似于計(jì)數(shù)型抽樣的LQ抽樣方案。取值不是四舍五入，而是要往前取，才能保證準(zhǔn)確性Quality

control

and

reliability

handbook

H108-SamplingProcedures

and

Tables

for

life

and

Reliability

TestingChaper16，

P602Sampling

procedures

and

tables

for

life

and

reliability

testing(based

on

exponential

distribution)Select

22

items

randomly

from

a

lot

and

place

them

on

testing.Whenever

an

item

fails,

replace

it

with

another

item

randomlyselected

from

the

lot.If

the

test

continues

for

500

hour

with

no

more

than

2

failures,accepted

the

lot.If

3

failures

occur

before

the

500h

of

testing,

reject

the

lot.壽命試驗(yàn)抽樣的OC曲線T：Test

item

hours:

22X500=11000

hrs.Acceptance

criteria:

2Suppose

the

probability

of

a

failure

is

thesame

for

every

item

hour.So

this

is

a

sampling

plan

withn=11000and

c=2.OC

curve：

the

relationship

betweenacceptance

probability

and

mean

life

(1/λ)Calculation

of

OC

curve0.0001X11000=1.1,OCcurveProducer’s

risk

and

customer’s

riskH108:

producer’s

risk

of

0.1

of

rejecting

a

lot

that

has

a

mean

life

of

10000

hrs.Also

about

0.1

for

the

consumer’s

risk

of

accepting

a

lot

that

has

a

mean

life

of

2000

hrs.Item

hours

required

for

acceptance=items

testedX500

(500

hrs.

required

)All

Risk=0.1,

500

hrs.0.910.040.90.0880.90.0910.9030.0870.9010.097Experiment

to

illustrate

certain

aspects

of

aconstant

failure

rateFor

example:To

use

twoJapaneseIcosahedral

dice

to

get

a0.02

failure

rate,00

or

99

defined

as

failure.Probability

offailure:2/20X2/20+2/20X2/20=0.02Rearrange

of

the

data:

a

lifetestexample

without

replacementEstimated

λ=number

of

failures

observed

/

number

of

item

hours

oftestEstimated

θ=number

of

item

hours

up

to

the

t