Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula

2020 ◽  
Vol 204 ◽  
pp. 107168
Author(s):  
Fuqiang Sun ◽  
Fangyou Fu ◽  
Haitao Liao ◽  
Dan Xu
2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Li Sun ◽  
Xiaohui Gu ◽  
Pu Song

It is assumed that the drift parameter is dependent on the acceleration variables and the diffusion coefficient remains the same across the whole accelerated degradation test (ADT) in most of the literature based on Wiener process. However, the diffusion coefficient variation would also become obvious in some applications with the stress increasing. Aiming at the phenomenon, the paper concludes that both the drift parameter and the diffusion parameter depend on stress variables based on the invariance principle of failure mechanism and Nelson assumption. Accordingly, constant stress accelerated degradation process (CSADP) and step stress accelerated degradation process (SSADP) with random effects are modeled. The unknown parameters in the established model are estimated based on the property of degradation and degradation increment, separately for CASDT and SSADT, by the maximum likelihood estimation approach with measurement error. In addition, the simulation steps of accelerated degradation data are provided and simulated step stress accelerated degradation data is designed to validate the proposed model compared to other models. Finally, a case study of CSADT is conducted to demonstrate the benefits of our model in the practical engineering.


2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su

The population and individual reliability assessment are discussed, and a Bayesian framework is proposed to integrate the population degradation information and individual degradation data. Different from fixed effect Wiener process modeling, the population degradation path is characterized by a random effect Wiener process, and the model can capture sources of uncertainty including unit to unit variation and time correlated structure. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters in the population model. To achieve individual reliability assessment, we exploit a Bayesian updating method, by which the unknown parameters are updated iteratively. Based on updated results, the residual use life and reliability evaluation are obtained. A lasers data example is given to demonstrate the usefulness and validity of the proposed model and method.


Author(s):  
Zhiao Zhao ◽  
Yong Zhang ◽  
Guanjun Liu ◽  
Jing Qiu

Sample allocation and selection technology is of great significance in the test plan design of prognostics validation. Considering the existing researches, the importance of prognostics samples of different moments is not considered in the degradation process of a single failure. Normally, prognostics samples are generated under the same time interval mechanism. However, a prognostics system may have low prognostics accuracy because of the small quantity of failure degradation and measurement randomness in the early stage of a failure degradation process. Historical degradation data onto equipment failure modes are collected, and the degradation process model based on the multi-stage Wiener process is established. Based on the multi-stage Wiener process model, we choose four parameters to describe different degradation stages in a degradation process. According to four parameters, the sample selection weight of each degradation stage is calculated and the weight of each degradation stage is used to select prognostics samples. Taking a bearing wear fault of a helicopter transmission device as an example, its degradation process is established and sample selection weights are calculated. According to the sample selection weight of each degradation process, we accomplish the prognostics sample selection of the bearing wear fault. The results show that the prognostics sample selection method proposed in this article has good applicability.


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