Correlation analysis of degrading systems based on bivariate Wiener processes under imperfect maintenance

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2024-07-02 DOI:10.1002/asmb.2883

Lucía Bautista, Inma T. Castro, Christophe Bérenguer, Olivier Gaudoin, Laurent Doyen

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引用次数: 0

Abstract

This article focuses on the correlation between the degradation levels of the two components that form a system. The degradation evolution of each component is modeled using Wiener processes. Both components are dependent and this dependence is described using the trivariate reduction method. To reduce the degradation and extend the system lifetime, preventive maintenance actions are periodically performed. These preventive maintenance actions are imperfect and they are modeled by using an arithmetic reduction of degradation of infinite order model with a determined maintenance efficiency parameter. The evolution of the maintained system is analysed by assessing the expectation and variance of both degradation processes at successive maintenance times. The novelty of this work is the analysis of the Pearson correlation coefficient between the degradation levels of the two components. Different properties of the monotonicity of the Pearson correlation coefficient between the two degradation paths are obtained by considering equal maintenance efficiency and equal general time scales functions for the two Wiener degradation processes associated to each degrading component.

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不完善维护条件下基于双变量维纳过程的退化系统相关性分析

本文重点讨论构成系统的两个组件的退化程度之间的相关性。每个组件的退化演化过程都使用维纳过程建模。两个组件之间存在依赖关系，这种依赖关系使用三变量还原法进行描述。为了减少退化并延长系统寿命，需要定期进行预防性维护。这些预防性维护行动是不完美的，它们是通过使用算术还原退化的无穷阶模型和一个确定的维护效率参数来建模的。通过评估连续维护时间内两个退化过程的期望值和方差，对维护系统的演变进行分析。这项工作的新颖之处在于分析了两个组件退化水平之间的皮尔逊相关系数。通过考虑与每个退化部件相关的两个维纳退化过程的相同维护效率和相同一般时间尺度函数，可以获得两个退化路径之间的皮尔逊相关系数的不同单调性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.