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.

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.

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.

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