学术 型海报模板

ACKNOWLEGEMENT
This work is supported by the National Natural Science Foundation of China (Grant No. xxxxxxxx).
BIOGRAGHY xxxxxx
He is currently a Ph.D. candidate at the School of xxxxxx, xxxxxx University. His research interests include xxxxxx.
Gamma
TGamma
Normal
Parameter Average Variance
14 2 26
56
7 4 24 112
4 7 21 196
14 2 30
56
7 4 32 112
4 7 35 196
28 7.5 28
56
28 10.5 Leabharlann Baidu8 112
28 14 28 196
Results considering dispersion
Normal and Gamma distribution with different parameters are chosen to study the influence of individual dispersion on reliability.
Type Parameter
Normal
INTRODUCTION
Reliability tests are usually conducted at a certain virtual environmental stress level whereas the field environment is highly varied from the virtual environment. This paper presents a novel method of field reliability prediction considering environment variation and product individual dispersion. Wiener diffusion process with drift was used for degradation modeling and a link function which presents degradation rate is introduced to model the impact of varied environment and individual dispersion. Results indicates that properly modeled (proper distribution type and parameters) environmental stress is the fundamental of varied environment oriented reliability prediction.
and a.
Five units were subjected to an
accelerated degradation test at
each of 60°C, 85°C , 110°C and
140°C. The degradation data for
each unit was observed at t1=100, t2=200, t3=300, t4=400, t5=500, t6=600, t7=700, t8=800, t9=900, t10=1000 (in hours).
distribution to the parameter z and a .
The reliability function follows
R t aU zU R t | z, a f z f adzda aL zL
where f z and f a are density functions for z
The first time that the degradation process crosses the critical threshold value D follows an Inverse Gaussian distribution, and the reliability function can be given as
Gamma, transformed Gamma and Normal distribution with different parameters are chosen to study the influence of temperature on reliability.
Type
Probability Density
R(t
)
D
t
(t)
exp
2 D 2t
(t
)
D
t
(t
)
Assume xi (tij ) is the degradation value of the ith product at time tij , then
xij B(tij ) ij ~ N (ij , 2tij )
degradation rate with a link function such as
the Arrhenius relationship
z aeb z
The varied environmental factors and individual dispersion can be modelled by giving a
and
f (xij )
1
xij
ij
tij tij
The effect that environmental factors z and
individual dispersion have on degradation
process can be considered as changes in the
Degradation modelling
Case
Results
Wiener process is a widely used method in degradation process and can be seen as a degradation rate model.
X (t) B(t) (t)
The reliability curve calculated by the method presented in this paper is rather different from the results by taking the average of environmental factors and different parameters for the same distribution have obvious impact on reliability. Under the condition of same average and variance, the curves of Gamma, T-Gamma, and Normal distributed temperature is different too.
CONCLUSION
Gamma, transformed-Gamma (T-Gamma) and Normal distribution with different parameters are employed to model right-skewed, left-skewed and symmetric stress distribution. Results show obvious difference in reliability, failure intensity and failure rate between varied stress and constant stress situation and each other. It indicates that properly modeled (proper distribution type and parameters) environmental stress is the fundamental of varied environment oriented reliability prediction. In a linear drift degradation process and Arrhenius-type link function situation, it is reasonable not concerning about product individual dispersion because the impact is barely small, while other situations can be studied in the same way proposed in this present paper.
N ,
(200,15) (200,10) (200,5)
Gamma (4,2/15,170)
, , (9,3/10,170)
(36,6/5,170)
Average
200 200 200 200 200 200
Variance
225 100 25 225 100 25
Under the same stress distribution, reliability curves of different individual dispersion situations with the same average value are almost the same, showing no significant variance.