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.

Synthetic Reliability Assessment Model involving Temperature–Humidity Step-Stress Based on Wiener Process

2020 ◽  
pp. 2150016
Author(s):  
Bin Suo ◽  
Liang Zhao
Keyword(s):  
Wiener Process ◽  
High Reliability ◽  
Likelihood Estimation ◽  
Degradation Process ◽  
Test Sample ◽  
Assessment Model ◽  
Engineering Practice ◽  
Accelerated Degradation ◽  
Failure Data ◽  
Newton Iteration Method

There are always some difficulties in storage reliability evaluation of high-reliability, long-life, and high-value products, such as the test sample being small, degradation speed being slow, and failure data being inadequate. Temperature–humidity step-stress accelerated degradation test (THSS-ADT) is an effective method to evaluate the reliability of this type of products, but the test data processing is an extremely complex work. The motivation of this paper is to provide a clear, effective, and convenient method to evaluate the reliability on the basis of THSS-ADT data. Considering the stochastic volatility in degradation process, Wiener process is used to modeling the accelerated degradation process. The methods to estimate the parameters of Peck accelerated model and degradation model are discussed under temperature–humidity step-stress. As ordinary optimization algorithms (such as Newton Iteration Method and impelling function method) find it difficult to get the solutions, particle swarm optimization (PSO) method is used to solve the problem of maximum-likelihood estimation. Finally, the proposed methods are demonstrated for two examples, in which one is a numerical simulation, and another is an engineering practice of a microwave power amplifier.

scholarly journals Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su
Keyword(s):  
Nonlinear Diffusion ◽  
Goodness Of Fit ◽  
Real Data ◽  
Degradation Process ◽  
Copula Function ◽  
Assessment Method ◽  
Unknown Parameters ◽  
Degradation Data ◽  
Proposed Model ◽  
Frank Copula

A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

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.

scholarly journals Optimization of the Accelerated Degradation Test Plan for Electrical Connector Contact Pairs Based on a Nonlinear Wiener Process

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ping Qian ◽  
Lei Hong ◽  
Wenhua Chen ◽  
Yongwang Qian ◽  
Zhe Wang ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Wiener Process ◽  
Stress Level ◽  
Test Plan ◽  
Accelerated Degradation ◽  
Stress Levels ◽  
Degradation Test ◽  
Accelerated Degradation Test ◽  
Stress Dependent ◽  
Drift Coefficient

Accelerated degradation test is an effective method to evaluate the reliability of products with long life and high reliability. The performance of most products fluctuates randomly in the degradation process, so it is suitable to use Wiener process. At present, the diffusion coefficient is regarded as constant in Wiener process, while the drift coefficient is related to stress. However, in practice, the amplitude of product performance fluctuation increases with the increase of stress level, which is not constant. Therefore, for the nonlinear Wiener case where both the drift coefficient and the diffusion coefficient are stress dependent, this paper studies the constant-stress accelerated degradation test theories and methods. Taking the contact pairs of electrical connectors as the research object, the minimum variance of reliable life estimate under normal stress is taken as the target. After determining the censored time at each stress level, the test stress level, the sample distribution ratio at each stress level, and the test interval at the one-third power scale of time are taken as design variables. The test plan under 3, 4, and 5 stress levels is optimized and compared with the general test plan. The influence of the difference between high and low stress levels on the evaluation accuracy is analyzed. Finally, the sensitivity analysis of parameters shows that the optimization plan has good robustness, and the change of stress quantity has little influence on the robustness of the plan.

A nonlinear Wiener degradation model integrating degradation data under accelerated stresses and real operating environment

2020 ◽  
pp. 1748006X2097809
Author(s):  
Li Sun ◽  
Fangchao Zhao ◽  
Narayanaswamy Balakrishnan ◽  
Honggen Zhou ◽  
Xiaohui Gu
Keyword(s):  
Remaining Useful Life ◽  
Normal Stresses ◽  
Operating Environment ◽  
Unknown Parameters ◽  
Step Method ◽  
Degradation Model ◽  
Accelerated Degradation ◽  
Degradation Data ◽  
Proposed Model ◽  
The Difference

Remaining useful life (RUL) prediction in real operating environment (ROE) plays an important role in condition-based maintenance. However, the life information in ROE is limited, especially for some long-life products. In such cases, accelerated degradation test (ADT) is an effective method to collect data and then the accelerated degradation data are converted to normal level of accelerated stresses through acceleration factors. However, the stresses in ROE are different from normal stresses since there are some other stresses except normal stresses, which cannot be accelerated, but still have impact on the degradation. To predict the RUL in ROE, a nonlinear Wiener degradation model is proposed based on failure mechanism invariant principle which is the precondition and requirement of an ADT and a calibration factor is introduced to calibrate the difference between ROE and normal stresses. Moreover, the unit-to-unit variability is considered in the concern model. Based upon the proposed approach, the RUL distribution is derived in closed form. The unknown parameters in the model are obtained by a new two-step method through fuzing converted degradation data in normal stresses and degradation data in ROE. Finally, the validity of the proposed model is demonstrated through several simulation data and a case study.

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