Bivariate degradation analysis of products based on Wiener processes and copulas

Pan, Zhengqiang; Balakrishnan, N.; Sun, Quan; Jing-lun, Zhou

doi:10.1080/00949655.2012.658805

Cited by 112 publications

(61 citation statements)

References 17 publications

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“…[26] To characterize the performance of a rubidium discharge lamp, both the rubidium consumption and the intensity reduction of the lamp need to be taken into account. [27] Moreover, due to the common influence from the external and internal environments, these PCs may be dependent. As such, to estimate the RL of a product with multiple PCs, proper multivariate degradation models need to be constructed first to capture the degradation of PCs over time.…”

Section: Introductionmentioning

confidence: 99%

Residual life estimation based on nonlinear-multivariate Wiener processes

Wang

2014

Journal of Statistical Computation and Simulation

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For some operable products with critical reliability constraints, it is important to estimate accurately their residual lives so that maintenance actions can be arranged suitably and efficiently. In the literature, most publications have dealt with this issue by only considering one-dimensional degradation data. However, this may be not reasonable in situations wherein a product may have two or more performance characteristics (PCs). In such situations, multi-dimensional degradation data should be taken into account. Here, for the target product with multivariate PCs, methods of residual life (RL) estimation are developed. This is done with the assumption that the degradation of PCs over time is governed by a multivariate Wiener process with nonlinear drifts. Both the population-based degradation information and the degradation history of the target product up-to-date are combined to estimate the RL of the product. Specifically, the populationbased degradation information is first used to obtain the estimates of the unknown parameters of the model through the EM algorithm. Then, the degradation history of the target product is adopted to update the degradation model, based on which the RL is estimated accordingly. To illustrate the validity and the usefulness of the proposed method, a numerical example about fatigue cracks is finally presented and analysed.

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Section: Introductionmentioning

confidence: 99%

Residual life estimation based on nonlinear-multivariate Wiener processes

Wang

2014

Journal of Statistical Computation and Simulation

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“…A detailed review of copulas can be found in Nelsen [1]. Some works on copula based reliability analysis are in [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Multivariate copula based dynamic reliability modeling with application to weighted-k-out-of-n systems of dependent components

Eryılmaz

2014

Structural Safety

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“…In addition, as a result of uncertain random factors in the testing environment, there is a rising trend in the curve in Figure 1. In light of the above features of the bearing relative temperature, we used the Wiener process for modeling [6][7][8][9][10][11]. This mathematical model can be expressed as follows:…”

Section: Degradation Modelmentioning

confidence: 99%

“…A numerical study and a case study of Li-ion batteries were carried out to illustrate and demonstrate the proposed prognostic method. Pan et al [6][7][8] analyzed product reliability using accelerated degradation modeling based on Wiener and gamma processes with fewer pan re-products. Zheng et al [5] built a nonlinear degradation model based on a nonlinear diffusion degradation process to incorporate the uncertainty measurement and the unit-to-unit variability into the estimated RUL.…”

Section: Introductionmentioning

confidence: 99%

“…Integrating the influence of uncertainty measurement and individual differences into reliability analysis to achieve more accurate reliability analysis of stochastic degradation systems is worth studying. In recent years, many scholars have been devoted to this [1][2][3][4][5][6][7][8]. Zhang [4] models the degradation state evolution of a system through a diffusion process with piecewise but time-dependent drift coefficient functions.…”

Section: Introductionmentioning

confidence: 99%

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Reliability Analysis of the High-speed Train Bearing Based on Wiener Process

Zhu

Nan

2018

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Abstract:Because of the existence of uncertainty measurement in the process of bearings degradation, it is difficult to carry out the reliability analysis. The random performance degradation model is used to analyze the reliability life of high-speed train bearing with the characteristics of slow degradation process and relatively stable degradation path. The unknown coefficients are viewed as random variables in the model. According to the analysis to a bearing testing data, the reliability analysis of the bearing life is finally completed. The results show that the method can assess reliability of the bearing life with zero failure by taking full advantage of the performance degradation data in the small sample size.

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Bivariate degradation analysis of products based on Wiener processes and copulas

Cited by 112 publications

References 17 publications

Residual life estimation based on nonlinear-multivariate Wiener processes

Residual life estimation based on nonlinear-multivariate Wiener processes

Multivariate copula based dynamic reliability modeling with application to weighted-k-out-of-n systems of dependent components

Reliability Analysis of the High-speed Train Bearing Based on Wiener Process

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