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產(chǎn)品壽命期望值MTTF及L10之計(jì)算

2019-07-11 09:11:40    責(zé)任編輯: 百度百科     0

產(chǎn)品壽命期望值MTTF及L10之計(jì)算

1.產(chǎn)品壽命期望值MTTF是指產(chǎn)品發(fā)生63.2%不良時(shí)之預(yù)期時(shí)間,或稱信賴度36.8%之時(shí)間。

產(chǎn)品壽命期望值L10是指產(chǎn)品發(fā)生10%不良時(shí)之預(yù)期時(shí)間,或稱信賴度90%之時(shí)間。

MTTF=t1+(t2-t1)*0.632

L10=t1+(t2-t1)*0.1

t1:達(dá)不良率值最短時(shí)間

t2:達(dá)不良率值最長(zhǎng)時(shí)間

2.所請(qǐng)不良之定義并無(wú)一定之規(guī)范,譬如:

(1)可以用一批產(chǎn)品作測(cè)試,經(jīng)2000,3000,5000,10000,18000小時(shí)后測(cè)試其轉(zhuǎn)速、消耗電流是否超出規(guī)格做為不良之定義。

(2)或以精密測(cè)量?jī)x器測(cè)量軸心潤(rùn)滑油料殘余量剩多少為不良之定義。 

3.測(cè)試之樣品數(shù)越多則數(shù)據(jù)越可靠,最少三個(gè)。

4.測(cè)試時(shí)間可以2000,3000,5000,10000,18000小時(shí)做為規(guī)范。也就是說(shuō)測(cè)試時(shí)間點(diǎn)i為1,2,….n,因測(cè)試點(diǎn)有五點(diǎn),所以n=5,I=1,2,3,4,5 共五點(diǎn)。

 

i

1

2

3

4

5

t (小時(shí))

2000

3000

5000

10000

18000







 

5. 假設(shè)現(xiàn)有一風(fēng)扇產(chǎn)品,以軸心油料消耗至50%時(shí)即視為不良,因油料耗至50%時(shí)間相當(dāng)長(zhǎng),故必需以外差法求其時(shí)間。
若油料損耗曲線趨近線性,油耗公式可寫(xiě)為Y=Ax+b
Y:經(jīng)過(guò)i時(shí)間后油指殘余量
X:時(shí)間(單位:小時(shí))
a:曲線斜率。等于Σ(Xi-X)*(Yi-Y)/ Σ(Xi-X)2
b:常數(shù)(單位:%)等于Y-[Σ(Xi-X)*(Yi-Y)/ Σ(Xi-X)2]*X=Y-Ax
注:計(jì)算時(shí),若b>100%以100%計(jì)算
X:=各測(cè)試時(shí)間點(diǎn)之平均值
=(2000+3000+5000+10000+18000)/5=7600小時(shí)
Y:各測(cè)試時(shí)間點(diǎn)油脂殘余量平均值,假設(shè)有三個(gè)樣品S1、S2、S3經(jīng)過(guò)i時(shí)間其油脂殘余量如下:

 

Xi(小時(shí))

2000

3000

5000

10000

18000

S1(%)

99.9

99.8

99.6

99.1

98

S1(%)

99.5

99.2

97

93

87

S1(%)

99.5

99.3

98

96

93







 

(1) S1樣品
X=7600,Y=(99.9+99.8+99.6+99.1+98)/5=99.28%
a=[(2000-7600)(99.9-99.28)+(3000-7600)(99.8-99.28)+(5000-7600)(99.6-99.28)+(10000-7600)(9931-99.28)+(18000-7600)(98-99.28)]/[(2000-7600)2+(3000-7600)2+(5000-7600)2+(10000-7600)2+(18000-7600)2]=[(-3472)+(-2392)+(-832)+(-432)+(-13312)]/[(31360000)+(21160000)+(6760000)+(108160000)]=-20440/167440000=-0.000122
b=Y-aX=99.28-(-0.000122*7600)=99.28+0.927=100.2(%),以100(%)計(jì)算
依據(jù)油耗公式Y(jié)=aX+b,得知S1風(fēng)扇在潤(rùn)滑油量(Y)剩50%之時(shí)間X;
X=(Y-b)/a=(50-100)/(-0.000122)=-50/(-0.000122)=409836小時(shí)
(2) S2樣品
X=7600,Y=(99.5+99.2+97+93+87)/5=95.14%
a=[(2000-7600)(99.5-95.14)+(3000-7600)(99.2-95.14)+(5000-7600)(97-95.14)+(10000-7600)(9.-95.14)+(18000-7600)(87-95.14)]/ [(2000-7600)2+(3000-7600)2+(5000-7600)2+(10000-7600)2+(18000-7600)2]=[(-24420)+(-18680)+(-4840)+(-5140)+(-84660)]/[(31360000)+(21160000)+(6760000)+(108160000)]=-137740/167440000=-0.0008226
b=Y-aX=95.14-(-0.0008226*7600)=95.14+6.25=101.39(%),以100%計(jì)算
依據(jù)油耗公式Y(jié)=aX+b,得知S2風(fēng)扇在潤(rùn)滑油量(Y)剩50%之時(shí)間X:
X=(Y-b)/a=(50-100)/(-0.0008226)=-50/(-0.0008226)=60782小時(shí)
(3) S3樣品
X=7600,Y=(99.5+99.3+98+96+93)/5=97.16%
a=[(2000-7600)(99.5-97.16)+(3000-7600)(99.3-97.16)+(5000-7600)(98-97.16)+(10000-7600)(96-97.16)+(18000-7600)(93-97.16)]/ [(2000-7600)2+(3000-7600)2+(5000-7600)2+(10000-7600)2+(18000-7600)2]=[(-13104)+(-9844)+(-2184)+(-2784)+(-43264)]/[(31360000)+(21160000)+(6760000)+(108160000)]=-71180/167440000=-0.0004251
b=Y-aX=0.90-(-0.0004251*7600)=97.14+3.23=100.37(%),以100%計(jì)算
依據(jù)油耗公式Y(jié)=aX+b,得知S3風(fēng)扇在潤(rùn)滑油量(Y)剩50%之時(shí)間X:
X=(Y-b)/a=(50-100)/(-0.0004251)=-50/(-0.0004251)=117619小時(shí)

6.由以上三樣品得知:
油料最先消耗50%的風(fēng)扇為S2,時(shí)間為60782小時(shí)
最慢者為S1,時(shí)間409836小時(shí)
所以得知t1=60782小時(shí),t2=409836小時(shí)
7.MTTF=t1+(t2-t1)*0.632=60782+(409836-60782)*0.632=60782+220602=281384小時(shí)
L10=t1+(t2-t1)*0.1=60782+(409836-60782)*0.1=60782+34905=95687小時(shí)

 

L10 Expectancy: 50,000 hours minimum@ fan rated voltage and the temperature of 40℃, According to the equation for  Arrhenius model, MTTF ≒ 7×L10 = 350,000 hours. And we rely on a zero failure test strategy and accelerated testing technique, to determine the total test time (t) for verifying the above life estimation by the equations,

t = 1.036×MTTF×[(Br;c)÷ n]0.91÷AF , and AF = 2(Ts-Tu)/10

where, (Br;c) is Poisson distribution factor with the failure number of r equal to 0 and the decimal confidence level of c equal to 0.90(90%), and
Stress/ Elevated Temperature    Ts (℃) Unstress Temperature    Tu (℃) Acceleration Factor   
AF Quantity of Test Devices                  
n (pcs) Poisson Distribution Factor            
Br;c Required test time with zero failure                     t  (hours) Actual test time with zero failure         
t (hours) Verified MTTF 40 ℃         
(hours) Verified L10      40 ℃        (hours)
90 40 32 30 2.303 11,428 1,200 383,234

 

 


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