学术 型海报模板ppt课件

Type
Probability Density
Gamma
TGamma
Normal
Parameter Average Var 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 28 112
28 14 28 196
Assume
is the degradation value of the ith
product at time , then
and
The effect that environmental factors and individual dispersion have on degradation process can be considered as changes in the degradation rate with a link function such as the Arrhenius relationship
where
and a.
and are density functions for z
Gamma, transformed Gamma and Normal distribution with different parameters are chosen to study the influence of temperature on reliability.
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.
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.
The varied environmental factors and individual dispersion can be modelled by giving a
distribution to the parameter z and a .
The reliability function follows
Results considering dispersion
Normal and Gamma distribution with different parameters are chosen to study the influence of individual dispersion on reliability.
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).
Degradation modelling
Case
Results
Wiener process is a widely used method in degradation process and can be seen as a degradation rate model.
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