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www.Weibull.com
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QALT 3
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QALT 10
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QALT 11
4
5<
4-<
➫ 4-<
Average Use = 10 hours a week!
1 Week = 168 hr
Possible Acceleration Factor = 16
QALT 12
(
4-<
➫ 242
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QALT 13
2
8
➫ #
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QALT 16
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QALT 17
#
S tre ss
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QALT 19
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Life=exp(a/stress)
QALT 21
➫ #'(
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%
QALT 22
3## .
➫ *($7(%
➫ 5$%
Probability Plot
Unreliability, F(t)
99.00
50.00
10.00
5.00
1.00
0.01
0.10
1.00
10.00
100.00 1000.00 10000.00
Time, (t)
QALT 23
## 5
QALT 24
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➫ $%(
➫ 3($%
➫ 3($%
QALT 25
Probability Plot
➫
-
*(
&
Probability Plot
$"
99.90
10.00
5.00
1.00
0.50
0.10
0.05
0.01
10.00
68.00
126.00 184.00 242.00 300.00
Time, (t)
50.00
7(
10.00
Probability Plot
99.90
"
5.00
1.00
0.50
0.10
0.05
0.01
10.00
100.00
Time, (t)
1000.00
"
Unreliability, F(t)
Unreliability, F(t)
50.00
Reliability, R(t)
*(
100.00
50.00
10.00
5.00
1.00
0.50
0.10
0.05
0.01
10.00
100.00
1000.00
Time, (t)
QALT 26
5
➫
$%(
( #
QALT 27
7*(-8
➫ -'*('
(Mean, Median, R(x), F(x), λ, β, η, µ, σ)
Weibull Distribution with η() as a function of stress
QALT 28
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QALT 29
5(## 5
7(*(&5
R eliability vs Stress S urface
QALT 30
3## 5
➫ 5
-9
L(V ) = C ⋅ e
B
V
QALT 31
➫ 5
-9
1
L(V ) = ⋅ e
V
B

− A− 
 V
➫ )#5
-9
1
L(V ) =
n
K ⋅V
QALT 32
➫ 25
L(U ,V ) = A ⋅ e
φ b 
 + 
V U 
➫ 25
L(U , V ) =
C
n
U e
B
−
V
QALT 33
➫ #(
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'
(% (
(
0
#(
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;
QALT 34
5()
➫
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➫ (("
➫ (
➫ (#(#
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QALT 36
➫ (
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QALT 37
)
s ≠ f(t)
Stress is time independent!
QALT 38
*$" *%
Stress is time dependent!
(Quasi time independent)
s = f(t)
QALT 39
*$- *%
Stress is time dependent!
s = f(t)
QALT 40
)
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QALT 41
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L(V ) = C ⋅ e
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QALT 42
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B
ln( L(V )) = ln(C ) +
V
QALT 43
QALT 44
A Look at the Parameter B
➫ Depending
on the application (and
where the stress is exclusively
thermal), the parameter % can be
replaced by,
EA
activation energy
activation energy
B=
=
=
Boltzman's constant 8.623 × 10 −5 eV ⋅ K −1
K
QALT 45
A Look at the Parameter B,
cont.
➫
➫
➫
Note that in this formulation, the activation
energy must be known apriori.
If the activation energy is known then there is
only one model parameter remaining, &.
Because in most real life situations this is rarely
the case, all subsequent formulations will
assume that this activation energy is unknown
and treat % as one of the model parameters.
QALT 46
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➫%
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QALT 47
7(
β
f (t ) =
η
t
⋅  
η 
β −1
e
η = L(V ) = C ⋅ e
➫ .

β
 t
f (t , V ) =
⋅
B 
B

V
C ⋅ e  C ⋅ eV
t
− 
η 
β
B
V




β −1
e

 t
−
B

 C ⋅e V





β
QALT 48
QALT 49
/
➫ $%
(#
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LUSE
AF =
L Accelerated
➫ /'
AF =
LUSE
L Accelerated
=
C ⋅e
C ⋅e
B
Vu
B
VA
=
e
e
B
Vu
B
VA
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 B B
 −
V V
A
 u




QALT 50
&
➫
(
BA@C
.
β = 4.291
B = 1861.618
C = 58.984
QALT 51
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QALT 55
) ➫ 2
L(U ,V ) = A ⋅ e
φ b 
 + 
V U 
➫ L(U , V ) =
C
n
U e
−
B
V
QALT 56
Generated by: ReliaSoft's ALTA - www.ReliaSoft.com - 888-886-0410
Generated by: ReliaSoft's ALTA - www.ReliaSoft.com - 888-886-0410
Life vs Stress
Life vs Stress
Life
10000.00
Life
1000.00
100.00
1000.00
10.00
100.00
358.00
368.40
378.80
389.20
Temperature
399.60
410.00
0.20
1.00
Relative Humidity
QALT 57
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QALT 58
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QALT 59
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QALT 60
Probability Lognormal
Unreliability
99.00
IPL/Log
Data 2
90
F=6 | S=0
180
F=6 | S=0
50.00
➫ -
10.00
5.00
Adamantios Mettas
ReliaSoft Corp.
10/9/00
2:19:18 PM
1.00
1.00
10.00
Number of Cycles
Std=0.1459, K=1.1264E-5, n=1.8740
5
100.00
QALT 61
'
Life vs Stress
100.00
At 45o
Mean Life=71.6
At 45º Cycles
IPL/Log
Data 2
Median
Mean Life
45
F=12 | S=0
Acceleration Factor vs Stress
Life
20.00
IPL/Log
Data 2
45
F=12 | S=0
10.00
ReliaSoft Corp.
10/9/00
2:24:48 PM
1.00
10.00
100.00
Stress
1000.00
Std=0.1459, K=1.1264E-5, n=1.8740
Note that the base 45 data yielded
an MTTF estimate of 70.33 cycles
(utilizing a lognormal distribution).
Acceleration factor
16.00
12.00
8.00
4.00
ReliaSoft Corp.
10/9/00
2:21:02 PM
0
10.00
48.00
86.00
124.00
Stress
162.00
200.00
Std=0.1459, K=1.1264E-5, n=1.8740
QALT 62
#-G
➫ &H
9
(9.
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L( X ) = e
m

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 a 0 + ai X i 
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
i =1
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QALT 63
#-G
➫ &
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&&
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L(V (t )) = Ce
 B 
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 V (t ) 
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QALT 64
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➫ 3&(0.
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➫ 3
5 QALT 65