Reliability analysis for accelerated degradation data based on the Wiener process with random effects

2020 ◽  
Vol 36 (6) ◽  
pp. 1969-1981
Author(s):  
Xiaofei Wang ◽  
Bing Xing Wang ◽  
Wenhui Wu ◽  
Yili Hong
Keyword(s):  
Reliability Analysis ◽  
Wiener Process ◽  
Random Effects ◽  
Accelerated Degradation ◽  
Degradation Data

scholarly journals Accelerated Degradation Process Analysis Based on the Nonlinear Wiener Process with Covariates and Random Effects

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Li Sun ◽  
Xiaohui Gu ◽  
Pu Song
Keyword(s):  
Diffusion Coefficient ◽  
Wiener Process ◽  
Random Effects ◽  
Process Analysis ◽  
Likelihood Estimation ◽  
Degradation Process ◽  
Unknown Parameters ◽  
Accelerated Degradation ◽  
Degradation Data ◽  
Drift Parameter

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.

scholarly journals Accelerated Degradation Tests Modeling Based on the Nonlinear Wiener Process with Random Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shengjin Tang ◽  
Xiaosong Guo ◽  
Chuanqiang Yu ◽  
Haijian Xue ◽  
Zhijie Zhou
Keyword(s):  
Wiener Process ◽  
Random Effects ◽  
Process Modeling ◽  
High Reliability ◽  
Random Variable ◽  
Degradation Process ◽  
Unknown Parameters ◽  
Accelerated Degradation ◽  
Degradation Tests ◽  
Product Variation

Accelerated degradation tests (ADT) modeling is an important issue in lifetime assessment to the products with high reliability and long lifetime. Among the literature about the accelerated nonlinear degradation process modeling, the current methods did not consider the product-to-product variation of the products with the same type. Therefore, this paper proposes an accelerated degradation process modeling method with random effects for the nonlinear Wiener process. Firstly, we derive the lifetime distribution of the nonlinear Wiener process with random effects. Secondly, the nonlinear Wiener process is used to model the degradation process of a single stress, and the drift coefficient is considered as a random variable to describe the product-to-product variation. Using the random acceleration model, the random effects are incorporated into the constant stress ADT models and the step stress ADT models. Then, a two-step maximum likelihood estimation (MLE) method is presented to estimate the unknown parameters in the degradation models. Finally, a simulation study and a case study are provided to demonstrate the application and superiority of the proposed model.

Accurate reliability inference based on Wiener process with random effects for degradation data

2020 ◽  
Vol 193 ◽  
pp. 106631 ◽  
Author(s):  
Xiaofei Wang ◽  
Bing Xing Wang ◽  
Pei Hua Jiang ◽  
Yili Hong
Keyword(s):  
Wiener Process ◽  
Random Effects ◽  
Degradation Data

Sample selection of prognostics validation test based on multi-stage Wiener process

2018 ◽  
Vol 233 (4) ◽  
pp. 605-614
Author(s):  
Zhiao Zhao ◽  
Yong Zhang ◽  
Guanjun Liu ◽  
Jing Qiu
Keyword(s):  
Wiener Process ◽  
Process Model ◽  
Failure Modes ◽  
Early Stage ◽  
Sample Selection ◽  
Degradation Process ◽  
Time Interval ◽  
Degradation Data ◽  
Multi Stage ◽  
Selection Of

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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