A reliability evaluation method for multi-performance degradation products based on the Wiener process and Copula function

Pan, Guangze; Li, Yaqiu; Li, Xiaobing; Luo, Qin; Wang, Chunhui; Hu, Xianghong

doi:10.1016/j.microrel.2020.113758

Cited by 15 publications

(7 citation statements)

References 9 publications

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“…The function C captures all the dependence between the two components of the distribution F . We now come to the model used for instance in [7,8,9,19,24,25,35,37] (considering only the two-dimensional case as explained in the introduction), which is based on the use of such regular copulas to model the dependence between two univariate Lévy processes.…”

Section: Description Of the Modelmentioning

confidence: 99%

“…We now come to the model used for instance in References 18‐25 (considering only the two‐dimensional case as explained in the introduction), which is based on the use of such regular copulas to model the dependence between two univariate Lévy processes.…”

Section: The Three Modelsmentioning

confidence: 99%

“…See, e.g., [23] for more details about regular copulas. See, e.g., [7,8,9,19,24,25,35,37] for some papers considering regular copulas for modeling multivariate deterioration. See also [36, Section 7], which highlights the fact that this model has become more and more common in the reliability literature.…”

Section: Introductionmentioning

confidence: 99%

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On the modeling of dependence between univariate Lévy wear processes and impact on the reliability function

Mercier

Verdier

2022

Appl Stoch Models Bus & Ind

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Univariate Lévy processes have become quite common in the reliability literature for modeling accumulative deterioration. In case of correlated deterioration indicators, several possibilities have been suggested for modeling their dependence. The point of this paper is the study of three different dependence models: use of a regular copula, superposition of independent univariate Lévy processes and use of a Lévy copula. The three methods are first presented and analysed. In this way, it is shown that the multivariate process constructed through an ordinary copula cannot have independent increments in general, that is, it is not a Lévy process. The impact of a wrong choice for the model is next explored, based on data simulated from one model and next adjusted to all three models. It is shown that a wrong model can lead to either overestimate or underestimate the reliability function, which could be problematic in an application context.

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Section: Description Of the Modelmentioning

confidence: 99%

Section: The Three Modelsmentioning

confidence: 99%

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On the modeling of dependence between univariate Lévy wear processes and impact on the reliability function

Mercier

Verdier

2022

Appl Stoch Models Bus & Ind

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“…Zhang et al [17] proposed a method of bearing the remaining life based on the bivariate Wiener process and analyzed the correlation between the two performance indices by the Copula function. Guangze et al [18] proposed a multi-degradation modeling method based on a Wiener process and Copula function and took IGBT as an example to verify the model in engineering. However, there are only a few results of reliability correlation studies in the existing literature, and their research chiefly focuses on the field of reliability evaluation, assuming that the multi-parameter of the product obeys the same stochastic process, ignoring the inconsistent degradation laws of different performance parameters, which may lead to inaccurate assessments.…”

Section: Introductionmentioning

confidence: 99%

In-Orbit Reliability Evaluation of Space TWTA Based on Copula Function and Bivariate Hybrid Stochastic Processes

Wang

Ma³

et al. 2022

Applied Sciences

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Currently, it is still a challenge to study the degradation mechanisms of the space traveling wave tube amplifier (TWTA) with no failure and small sample tests. Given that the Copula functions are used to describe the correlation of multiple performance characteristics, this paper develops a bivariate hybrid stochastic degradation model to evaluate the in-orbit reliability of TWTA. Firstly, based on the impact analysis of the life of TWTA, helix current and anode voltage are selected as the performance degradation parameters. Secondly, stochastic processes with random effects based on the one-dimensional Wiener process and Gamma process are applied to describe the degradation of TWTA’s helix current and anode voltage, respectively, and the corresponding marginal distribution function is obtained. Then, the Copula function is utilized to describe the correlation between two different performance parameters of TWTA. Meanwhile, this paper also proposed a two-step method to estimate the reliability level of TWTA based on its in-orbit telemetry data through a two-step method, which contains a Markov Chain Monte Carlo (MCMC) algorithm and a maximum likelihood estimation (MLE) algorithm. Besides, the Bayes-Bootstrap sampling method is also used to improve the evaluation accuracy to overcome the defect of an in-orbit small sample of TWTA. Finally, a TWTA degradation case with a set of telemetry data is carried out, and the results show that the method proposed in this paper is more applicable and more accurate than other methods.

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“…A Copula function was then employed to explain the correlation between these degraded eigenvolumes. The degradation of a single performance parameter of a product was modeled by Pan et al 27 using a Wiener process, and the coupling of multiple performance parameters of a product was modeled using a Copula function. These models not only accurately described the coupling correlation between multiple performance degradations, but also provided a method for calculating the Copula function.…”

Section: Introductionmentioning

confidence: 99%

Multi-performance degradation reliability assessment method for a cabin door locking mechanism

Xie

Jiang

Han

et al. 2022

Advances in Mechanical Engineering

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A crucial part of the aircraft, the landing gear cabin door locking mechanism directly affects how well the landing gear retracts and how stealthily the aircraft operates. A reliability evaluation approach under multiple deterioration is provided, with a focus on the features of high reliability, small sample, and multiple performance degradation of the locking mechanism. The locking angle of the lock hook and the locking displacement offset of the lock hook are chosen as the characteristic quantities based on the analysis of the factors influencing the life of the locking mechanism; next, the Wiener process is used to model the degradation process of the selected characteristic quantities in order to obtain the failure probability density function for both; then, the multiple performance degradation reliability evaluation model is established using the Copula function, which can precisely and effectively characterize the coupled competitive relationships of multiple performance degradations. This model characterizes the stochastic correlation between the locking angle and the locking displacement of the lock hook. Following that, the Akaike information criteria (AIC) is used to choose the Copula function. Finally, the locking mechanism’s reliability assessment is carried out, as well as the evaluation findings are contrasted with those of the usual technique, which only takes into account a single failure performance characteristic quantity. A series of data analyses led to the conclusion that the approach is more relevant and accurate than that of the conventional method, and that it is not prudent to undervalue its dependability.

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A reliability evaluation method for multi-performance degradation products based on the Wiener process and Copula function

Cited by 15 publications

References 9 publications

On the modeling of dependence between univariate Lévy wear processes and impact on the reliability function

On the modeling of dependence between univariate Lévy wear processes and impact on the reliability function

In-Orbit Reliability Evaluation of Space TWTA Based on Copula Function and Bivariate Hybrid Stochastic Processes

Multi-performance degradation reliability assessment method for a cabin door locking mechanism

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