Extended cumulative exposure model, ecem
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The document discusses various reliability testing methodologies, including the Extended Cumulative Exposure Model (ECEM) and its application in predicting the lifespan of electrical devices under stress conditions. It emphasizes accelerated life testing techniques and provides mathematical models to estimate failure probabilities based on stress levels. The results are supported by simulations and data analysis, illustrating the effectiveness of the proposed models in reliability assessments.
![7
Fi(t)
F3(t)
F2(t)
F1(t)
time
broken
Fig. 2 Cumulative Probability Distributions Fj(t)
t1
s1
F2(s1) = F1(t1)
s1 = (t1 ! t0)
V1 ! Vth
V2 ! Vth
"
#
$ %
&
'
n
, V > Vth
= 0, V ( Vth
F0(t) = F2[(t ! t1) + s1], t1 ( t ( t2
F0(t) = 1! exp ! (t ! t1 + s1)
(V2 ! Vth)n
K
)
*
+
,
-
.
/
0
1
2
3
4
5"
#
$
$
%
&
'', V2 > Vth
= 0, V2 ( Vth
Sedyakin Model!
next stress level cdf model !](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-7-320.jpg)
![8
aa
･ † ･ †
Fi(t)
F3(t)
F2(t)
F1(t)
time
broken
Fig. 2 Cumulative Probability Distributions Fj(t)
t1
s1
F3(s2) = F2(t2 ! t1 + s1)
F0(t) = F3[(t ! t2) + s2], t2 " t " t3
s2 = (t2 ! t1 + s1)
V2 ! Vth
V3 ! Vth
#
$
% &
'
(
n
, V3 > Vth
= 0, V3 " Vth
F0(t) = 1! exp ! (t ! t2 + s2)
(V3 ! Vth)n
K
)
*
+
,
-
.
/
0
1
2
3
4
5#
$
%%
&
'
((, V3 > Vth
= 0, V3 " Vth
Sedyakin Model!
further next stress level cdf model !](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-8-320.jpg)
![9
aa
･ † ･ †
Fi(t)
F3(t)
F2(t)
F1(t)
time
broken
Fig. 2 Cumulative Probability Distributions Fj(t)
t1
s1
Fi(si!1) = Fi!1(ti!1 ! ti!2 + si!2)
F0(t) = Fi[(t ! ti!1) + si!1], ti!1 " t " ti
si!1 = (ti!1 ! ti!2 + si!2)
Vi!1 ! Vth
Vi ! Vth
#
$
% &
'
(
n
, Vi!1 > Vth
= 0, Vi!1 " Vth
F0(t) = 1! exp ! (t ! ti!1 + si!1)
(Vi ! Vth)n
K
)
*
+
,
-
.
/
0
1
2
3
4
5#
$
%
%
&
'
((
, Vi!1 > Vth
= 0, Vi!1 " Vth
Sedyakin Model!
highest stress level cdf model !](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-9-320.jpg)
![10
Cumulative probability
distribution F0
(t)
Fi(t)
F3(t)
F2(t)
F1(t)
time
broken
Fig. 2 Cumulative Probability Distributions Fj(t)
t1
s1
F0
(t)
t
Sedyakin Model!
by combining these models !
F(t,!) =1 " exp["{#(t)
$
}], ti"1 % t (! = (k,n,$)
T
)
!(t) =
t1 " t0
k / (v1 " vth)
n +
t2 " t1
k / (v2 " vth)
n +!+
t " ti "1
k / (vi " vth)
n
G0(t)
G0(t)
G0(t)](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-10-320.jpg)
![14
Tsuboi, Takami, Okabe, Inami, Aono, Transformer insulation reliability for moving oil with Weibull
analysis, IEEE Transactions on DEI, 17(3), 978 - 983. (2010)
0 cm/s 8 cm/s 16 cm/s
breakdownvoltage[kV]
mean
=90.2
mean
=80.1
mean
=79.8
Experimental Breakdown Voltage
BDV
low
BDV
mid
BDV
high](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-14-320.jpg)
![15
Cumulative Exposure Model, CEM
1.30 8.02 0.0098
0.913 9.52 0.0112
0.967 9.51 0.0114
0 cm/s 8 cm/s 16 cm/s
breakdownvoltage[kV]
mean
=90.2
mean
=80.1
mean
=79.8
BDV
low
BDV
mid
BDV
high
CEM explains this phenomena?
0 cm/s 8 cm/s 16 cm/s
mean 90.5 81.4 80.3
simulation using MLE](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-15-320.jpg)
![29
Experimental Breakdown Voltage
0 cm/s 8 cm/s 16 cm/s
breakdownvoltage[kV]
mean
=90.2
mean
=80.1
mean
=79.8
0 cm/s
8 cm/s
16 cm/s
!"#
$%&'()#*+),-%-&'&./
$%&'()#*+),-%-&'&./
!"#
G(t)
Fi(t)
!F1(t1)
F1(t1)
0%1&23#4
time
voltage
50
60
70
80
90
100
110
0 2 4 6 8 10 12
time
voltage
50
60
70
80
90
100
110
0 2 4 6 8 10 12
time
voltage
50
60
70
80
90
100
110
0 2 4 6 8 10 12](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-29-320.jpg)
![30
MLE for ECEM
1.30 8.02 0.0098
0.913 9.52 0.0112
0.967 9.51 0.0114
0 cm/s 8 cm/s 16 cm/s
breakdownvoltage[kV]
mean
=90.2
mean
=80.1
mean
=79.8
BDV
low
BDV
mid
BDV
high
ECEM explains this phenomena?
0 cm/s 8 cm/s 16 cm/s
mean 91.3 80.0 80.3
velocity
0 cm/s
8 cm/s
16 cm/s
1 1.30 8.02 0.0098
0.7 1.02 9.52 0.0117
0.5 1.10 9.33 0.0120
CEM
MM
simulation using MLE](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-30-320.jpg)
![34
Flaw of the IM
! = 0.5
!"!#
0.5
0
0
1
0.5 1t
$%$&'()*+(,(-./(
F2
F1
G(t)
! = 1
!"
0.5
0
0
1
0.5 1t
#$#%&'()*'+','
F2
F1
G(t)
F1(t)
F2(t)
0.5
0
0
1
0.5 1t
F1(t),F2(t)
! = 1
!"!# "!#
0.5
0
0
1
0.5 1t
$%$&'()*+(,(-./(
F2
F1
G(t)
! = 0
!"!# ##
0.5
0
0
1
0.5 1t
$%$&'()*+(,(-(
F2
F1
G(t)
BDV low? BDV mid? BDV high?
E[BDV]
=(1/4)*1+(1/2)* (1/2)*2
=3/2
E[BDV]
=(1/4)*1+(1/2)* (1/2)*2
=3/2
E[BDV]
=(1/4)*1+(1/2)* (1/2)*2
=3/2](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-34-320.jpg)
![35
Flaw of the IM
! = 0.5
!"!#
0.5
0
0
1
0.5 1t
$%$&'()*+(,(-./(
F2
F1
G(t)
! = 1
!"
0.5
0
0
1
0.5 1t
#$#%&'()*'+','
F2
F1
G(t)
F1(t)
F2(t)
0.5
0
0
1
0.5 1t
F1(t),F2(t)
! = 1
!"!# "!#
0.5
0
0
1
0.5 1t
$%$&'()*+(,(-./(
F2
F1
G(t)
! = 0
!"!# ##
0.5
0
0
1
0.5 1t
$%$&'()*+(,(-(
F2
F1
G(t)
BDV low? BDV mid? BDV high?
E[BDV]
=(1/2)*1+(1/2)*2
=3/2
E[BDV]
=(1/2)*1+(1/2)*2
=3/2
E[BDV]
=(1/2)*1+(1/2)*2
=3/2
E[BDV]
=(1/2)*1+(1/2)*2
=3/2](https://image.slidesharecdn.com/extendedcumulativeexposuremodelecem-151115084422-lva1-app6891/85/Extended-cumulative-exposure-model-ecem-35-320.jpg)
Extended cumulative exposure model, ecem
- 1. Hideo Hirose Department of Systems Design and Informatics, Kyushu Institute of Technology Fukuoka, 820-8502 Japan 1 On The Extended Cumulative Exposure Model, ECEM IEICE Reliability 2011.10.21
- 2. 2 Conventional V-t test log t log V threshold test data! extrapolation! Accelerated Life Test
- 3. 3 Weibull Power Law H. Hirose, (1986) Weibull Power Law Weibull Distribution Power Law
- 4. 4 Parameters are estimable H. Hirose, (1987)
- 5. 5 • 機器の信頼性試験 • 故障発生までに長時間を要する • 限られた試験時間内では故障発 生しない場合がある • 加速寿命試験 • 実使用時よりも厳しいストレス を加えて，機器の劣化を加速 → 評価時間の短縮 • 段階的上昇法 • 試験結果から機器の寿命を予測 1.ある一定時間，印加 2.非破壊なら印加電圧を上昇 3.破壊時の印加電圧を記録 • 30,30,45,35,... 電気機器の場合 H. Hirose, (2003) Step-up Voltage Test Step Stress Profile Testing. Using a step stress profile, test specimens are first subjected to a given level of stress for a preset period of time, and then they are subjected to a higher level of stress for a subsequent period of time. The process continues at ever increasing levels of stress, until either all the specimens fail, or the time period at the maximum stress level ends. This approach precipitates failures more rapidly for analysis. However, with this technique it is very difficult to properly model the acceleration and, hence, to quantitatively predict the item life under normal usage. Weibull Power Law
- 6. 6 Fi(t) F3(t) F2(t) F1(t) time broken Fig. 2 Cumulative Probability Distributions Fj(t) t1 s1 F0(t) = F1(t), 0 = t0 ! t ! t1 F0(t) = 1" exp " (V1 " Vth)n K # $ % & ' ( t ) * + , - . /0 1 22 3 4 55, V1 > Vth = 0, V1 ! Vth Sedyakin Model! lowest stress level cdf model !
- 7. 7 Fi(t) F3(t) F2(t) F1(t) time broken Fig. 2 Cumulative Probability Distributions Fj(t) t1 s1 F2(s1) = F1(t1) s1 = (t1 ! t0) V1 ! Vth V2 ! Vth " # $ % & ' n , V > Vth = 0, V ( Vth F0(t) = F2[(t ! t1) + s1], t1 ( t ( t2 F0(t) = 1! exp ! (t ! t1 + s1) (V2 ! Vth)n K ) * + , - . / 0 1 2 3 4 5" # $ $ % & '', V2 > Vth = 0, V2 ( Vth Sedyakin Model! next stress level cdf model !
- 8. 8 aa ･ † ･ † Fi(t) F3(t) F2(t) F1(t) time broken Fig. 2 Cumulative Probability Distributions Fj(t) t1 s1 F3(s2) = F2(t2 ! t1 + s1) F0(t) = F3[(t ! t2) + s2], t2 " t " t3 s2 = (t2 ! t1 + s1) V2 ! Vth V3 ! Vth # $ % & ' ( n , V3 > Vth = 0, V3 " Vth F0(t) = 1! exp ! (t ! t2 + s2) (V3 ! Vth)n K ) * + , - . / 0 1 2 3 4 5# $ %% & ' ((, V3 > Vth = 0, V3 " Vth Sedyakin Model! further next stress level cdf model !
- 9. 9 aa ･ † ･ † Fi(t) F3(t) F2(t) F1(t) time broken Fig. 2 Cumulative Probability Distributions Fj(t) t1 s1 Fi(si!1) = Fi!1(ti!1 ! ti!2 + si!2) F0(t) = Fi[(t ! ti!1) + si!1], ti!1 " t " ti si!1 = (ti!1 ! ti!2 + si!2) Vi!1 ! Vth Vi ! Vth # $ % & ' ( n , Vi!1 > Vth = 0, Vi!1 " Vth F0(t) = 1! exp ! (t ! ti!1 + si!1) (Vi ! Vth)n K ) * + , - . / 0 1 2 3 4 5# $ % % & ' (( , Vi!1 > Vth = 0, Vi!1 " Vth Sedyakin Model! highest stress level cdf model !
- 10. 10 Cumulative probability distribution F0 (t) Fi(t) F3(t) F2(t) F1(t) time broken Fig. 2 Cumulative Probability Distributions Fj(t) t1 s1 F0 (t) t Sedyakin Model! by combining these models ! F(t,!) =1 " exp["{#(t) $ }], ti"1 % t (! = (k,n,$) T ) !(t) = t1 " t0 k / (v1 " vth) n + t2 " t1 k / (v2 " vth) n +!+ t " ti "1 k / (vi " vth) n G0(t) G0(t) G0(t)
- 11. 11 W. Nelson, (1990). V. Bagdonavicius, M. Nikulin, (2001). !"# !"# $%&'()#*+),-%-&'&./ $%&'()#*+),-%-&'&./ G(t) Fi(t) Cumulative Exposure Model, CEM
- 12. 12 Simulated Breakdown Voltage Test n = 10" = 1 0 5 1 0 1 5 2 0 0 5 1 0 1 5 2 0 tim e Vs = 4 F(t j ) = 1 " exp{"#(t j ) $ } "(t j ) = k #1 $ %t $ (V1 n + V2 n + ! + Vj n )
- 14. 14 Tsuboi, Takami, Okabe, Inami, Aono, Transformer insulation reliability for moving oil with Weibull analysis, IEEE Transactions on DEI, 17(3), 978 - 983. (2010) 0 cm/s 8 cm/s 16 cm/s breakdownvoltage[kV] mean =90.2 mean =80.1 mean =79.8 Experimental Breakdown Voltage BDV low BDV mid BDV high
- 15. 15 Cumulative Exposure Model, CEM 1.30 8.02 0.0098 0.913 9.52 0.0112 0.967 9.51 0.0114 0 cm/s 8 cm/s 16 cm/s breakdownvoltage[kV] mean =90.2 mean =80.1 mean =79.8 BDV low BDV mid BDV high CEM explains this phenomena? 0 cm/s 8 cm/s 16 cm/s mean 90.5 81.4 80.3 simulation using MLE
- 16. 16 Extended CEM, ECEM !"# $%&'()#*+),-%-&'&./ $%&'()#*+),-%-&'&./ !"# G(t) Fi(t) !F1(t1) F1(t1) 0%1&23#4 Hideo. Hirose, (2011)proposed 0≦α≦1
- 18. 18 Relation among MM, ECEM, CEM !"# $%&'()#*+),-%-&'&./ $%&'()#*+),-%-&'&./ !"# G(t) Fi(t) !F1(t1) F1(t1) 0%1&23#4 α=0 α=0.5 α=1 ECEMMM CEM Memoryless Model Extended CEM Cumulative Exposure Model !"# $%&'()#*+),-%-&'&./ $%&'()#*+),-%-&'&./ Fi(t) BDV low BDV mid BDV highBDV low? BDV mid? BDV high?
- 19. 19 Relation among MM, ECEM, CEM !"# $%&'()#*+),-%-&'&./ $%&'()#*+),-%-&'&./ !"# G(t) Fi(t) !F1(t1) F1(t1) 0%1&23#4 α=0 α=0.5 α=1 ECEMMM CEM Memoryless Model Extended CEM Cumulative Exposure Model !"# $%&'()#*+),-%-&'&./ $%&'()#*+),-%-&'&./ Fi(t) BDV low BDV mid BDV high β=1 n=10 k=0.05235 0 cm/s 8 cm/s 16 cm/s mean 18.5 18.3 17.5
- 20. Likelihood ECEM Parameters Data Generation→Parameter Estimation (10,000 times) 4パラメータ×10,000個の推定結果を見て， うまく推定できるか調査 20 Model Validation by Simulation
- 21. ※典型的な絶縁機器 step-up test モデルパラメータ 履歴の残る割合 図 5: function G(t) for expansion of CEM Algorithm 1 Step-up voltage data generation algorithm while N samples do generate random number U repeat vi → vi+1 until U ≤ G(ti( j)) record v = vi end while 4 の3ケース 21 Random Number Generation
- 22. time voltage 10 12 14 16 18 20 22 l l l l l l l l l l ll l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 100 120 140 160 180 200 220 dataset1 input estimate dataset1 22 Simulation Procedure
- 23. time voltage 10 12 14 16 18 20 22 l l l l l l l l l l ll l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 100 120 140 160 180 200 220 dataset1 time voltage 10 12 14 16 18 20 22 l l l l l l l l l l ll l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 100 120 140 160 180 200 220 dataset2 input estimate dataset1 dataset2 23 Simulation Procedure
- 24. time voltage 10 12 14 16 18 20 22 l l l l l l l l l l ll l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 100 120 140 160 180 200 220 dataset1 time voltage 10 12 14 16 18 20 22 l l l l l l l l l l ll l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 100 120 140 160 180 200 220 dataset2 dataset1 dataset2 dataset10,000 time voltage 10 12 14 16 18 20 22 l l l l l l l l l l ll l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 100 120 140 160 180 200 220 dataset10,000 input estimate α=0.0, 0.5, 1.0 の3ケース 24 Simulation Procedure
- 25. 25 alpha count 0 500 1000 1500 2000 2500 3000 3500 0.0 0.2 0.4 0.6 0.8 beta count 0 200 400 600 800 1000 1200 1400 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 k count 0 500 1000 1500 2000 0.046 0.048 0.050 0.052 0.054 n count 0 1000 2000 3000 4000 5000 6000 7000 9 10 11 12 13 true value Simulation Result α＝0
- 26. n count 0 1000 2000 3000 4000 8 9 10 11 12 13 k count 0 200 400 600 800 1000 1200 1400 0.046 0.048 0.050 0.052 0.054 0.056 beta count 0 200 400 600 800 1000 1200 0.8 1.0 1.2 1.4 alpha count 0 200 400 600 800 1000 0.0 0.2 0.4 0.6 0.8 26 Simulation Result α＝0.5 true value
- 27. n count 0 1000 2000 3000 4000 5000 9.5 10.0 10.5 11.0 k count 0 500 1000 1500 0.051 0.052 0.053 0.054 0.055 0.056 0.057 alpha count 0 1000 2000 3000 4000 5000 0.95 0.96 0.97 0.98 0.99 1.00 1.01 beta count 0 200 400 600 800 1000 1200 1400 0.8 0.9 1.0 1.1 1.2 1.3 1.4 27 Simulation Result α＝1 true value
- 29. 29 Experimental Breakdown Voltage 0 cm/s 8 cm/s 16 cm/s breakdownvoltage[kV] mean =90.2 mean =80.1 mean =79.8 0 cm/s 8 cm/s 16 cm/s !"# $%&'()#*+),-%-&'&./ $%&'()#*+),-%-&'&./ !"# G(t) Fi(t) !F1(t1) F1(t1) 0%1&23#4 time voltage 50 60 70 80 90 100 110 0 2 4 6 8 10 12 time voltage 50 60 70 80 90 100 110 0 2 4 6 8 10 12 time voltage 50 60 70 80 90 100 110 0 2 4 6 8 10 12
- 30. 30 MLE for ECEM 1.30 8.02 0.0098 0.913 9.52 0.0112 0.967 9.51 0.0114 0 cm/s 8 cm/s 16 cm/s breakdownvoltage[kV] mean =90.2 mean =80.1 mean =79.8 BDV low BDV mid BDV high ECEM explains this phenomena? 0 cm/s 8 cm/s 16 cm/s mean 91.3 80.0 80.3 velocity 0 cm/s 8 cm/s 16 cm/s 1 1.30 8.02 0.0098 0.7 1.02 9.52 0.0117 0.5 1.10 9.33 0.0120 CEM MM simulation using MLE
- 31. velocity 0 cm/s 8 cm/s 16 cm/s 1 1.30 8.02 0.0098 0.7 1.02 9.52 0.0117 0.5 1.10 9.33 0.0120 31 CEM MM maximum likelihood parameters using profile log-likelihood Maximum Likelihood Parameters α 1 0.5 0.7 BDV low BDV high BDV low? BDV high?
- 32. 32 Relation among ECEM, CEM, MM ! = 1 !"!# "!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 0.5 !"!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 0 !"!# ## 0.5 0 0 1 0.5 1t $%$&'()*+(,(-( F2 F1 G(t) F1(t) F2(t) 0.5 0 0 1 0.5 1t F1(t),F2(t) BDV low BDV mid BDV high BDV low BDV mid BDV high
- 33. 33 Flaw of the IM ! = 0.5 !"!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 1 !" 0.5 0 0 1 0.5 1t #$#%&'()*'+',' F2 F1 G(t) F1(t) F2(t) 0.5 0 0 1 0.5 1t F1(t),F2(t) ! = 1 !"!# "!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 0 !"!# ## 0.5 0 0 1 0.5 1t $%$&'()*+(,(-( F2 F1 G(t) BDV low BDV mid BDV high BDV low BDV mid BDV high
- 34. 34 Flaw of the IM ! = 0.5 !"!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 1 !" 0.5 0 0 1 0.5 1t #$#%&'()*'+',' F2 F1 G(t) F1(t) F2(t) 0.5 0 0 1 0.5 1t F1(t),F2(t) ! = 1 !"!# "!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 0 !"!# ## 0.5 0 0 1 0.5 1t $%$&'()*+(,(-( F2 F1 G(t) BDV low? BDV mid? BDV high? E[BDV] =(1/4)*1+(1/2)* (1/2)*2 =3/2 E[BDV] =(1/4)*1+(1/2)* (1/2)*2 =3/2 E[BDV] =(1/4)*1+(1/2)* (1/2)*2 =3/2
- 35. 35 Flaw of the IM ! = 0.5 !"!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 1 !" 0.5 0 0 1 0.5 1t #$#%&'()*'+',' F2 F1 G(t) F1(t) F2(t) 0.5 0 0 1 0.5 1t F1(t),F2(t) ! = 1 !"!# "!# 0.5 0 0 1 0.5 1t $%$&'()*+(,(-./( F2 F1 G(t) ! = 0 !"!# ## 0.5 0 0 1 0.5 1t $%$&'()*+(,(-( F2 F1 G(t) BDV low? BDV mid? BDV high? E[BDV] =(1/2)*1+(1/2)*2 =3/2 E[BDV] =(1/2)*1+(1/2)*2 =3/2 E[BDV] =(1/2)*1+(1/2)*2 =3/2 E[BDV] =(1/2)*1+(1/2)*2 =3/2
- 36. • We have proposed a new model, extended cumulative exposure model, ECEM • The ECEM can explain the relation between the step- up voltage test result and the accelerated life test result • An experimental result is consistent with the proposed model • We have pointed out the flaw of the independence model, IM 36 Conclusion
- 37. Thank you Department of Systems Design and Informatics, Kyushu Institute of Technology Fukuoka, 820-8502 Japan 37 On The Extended Cumulative Exposure Model, ECEM IEICE Reliability 2011.10.21