scholarly journals A Bayesian Framework for Reliability Assessment via Wiener Process and MCMC

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su
Keyword(s):  
Wiener Process ◽  
Population Model ◽  
Random Effect ◽  
Reliability Assessment ◽  
Bayesian Framework ◽  
Mcmc Method ◽  
Unknown Parameters ◽  
Sources Of Uncertainty ◽  
Degradation Data ◽  
Proposed Model

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.

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.

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.

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.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

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.

Statistical methods of screening cut point determination in immunogenicity studies

Bioanalysis ◽  
2021 ◽  
Author(s):  
Meiyu Shen ◽  
Tianjiao Dai
Keyword(s):  
Random Effect ◽  
Random Effect Model ◽  
Covariance Structure ◽  
Repeated Measurements ◽  
Sources Of Uncertainty ◽  
Cut Point ◽  
Effect Model ◽  
Point Determination ◽  
Antidrug Antibodies ◽  
Immunogenicity Study

Background: Currently, screening cut point (CP) calculated from an assay validation with replicates are applied to an immunogenicity study with nonreplicates, for which the antidrug antibodies rate is determined. IID treats the replicate of a sample as coming from another independent sample. AVE uses average results from each sample across runs but inter-assay variability is reduced. Therefore, we propose a random effect model (REM) for calculating CP. Materials & method: We investigate impact of noncompatibility design between validation and immunogenicity studies on CP and compare these methods. Conclusion: IID may not fit for use when replicates’ variability dominates all sources of uncertainty. REM considers covariance structure of repeated measurements. CP by REM is smaller than that by IID but larger than that by AVE.

Valuation of machinery and equipment subject to the Wiener degradation process

2021 ◽  
Vol 57 (3) ◽  
pp. 97
Author(s):  
Sergey Smolyak
Keyword(s):  
Service Life ◽  
Wiener Process ◽  
Market Value ◽  
Degradation Process ◽  
Average Value ◽  
Boundary State ◽  
Proposed Model ◽  
Negative Drift ◽  
The Mean ◽  
The Moment

We propose a model describing the decrease in the market value of machines (depreciation) with age. Usually it is characterized by the percent good factor, i.e. the ratio of machine’s value to the value of similar new machinery item. Often, appraisers know about a used machinery item only by its age, but not its performance. Therefore, for the valuation of the machinery item of a known age, they have to use the mean (for machines of this age) of percent good factor. In the proposed model, the state of the machine is characterized by the intensity of the benefits it brings. In this case, the benefits from using the machine in a certain period are defined as the market value of the work performed by it minus operating costs. We describe the change in the intensity of benefits over time by the Wiener process with negative drift. This allows us to take into account the tendency for the performance of machine to deteriorate during operation. The market value of a machine is defined as the maximum mathematical expectation of the sum of discounted benefits from its use. It is shown that it corresponds to the moment the machine reaches a certain boundary state. The parameters of the Wiener process (drift and volatility) are expressed through the known characteristics of the machine's durability, namely the average value and the coefficient of variation of the service life. The dependences of the mean percent good factor of machines on the relative age (the ratio of age to the average service life) are found. It turned out that these dependencies are almost independent of the discount rate and average service life.

Reliability Assessment of Superluminescent Diodes from Performance Degradation Data

2010 ◽  
Vol 30 (10) ◽  
pp. 3044-3048 ◽  
Author(s):  
晁代宏 Chao Daihong ◽  
马静 Ma Jing ◽  
张春熹 Zhang Chunxi
Keyword(s):  
Reliability Assessment ◽  
Performance Degradation ◽  
Degradation Data ◽  
Superluminescent Diodes
Sign in / Sign up

Export Citation Format

Share Document