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A Copula Entropy Approach to Dependence Measurement for Multiple Degradation Processes

Science and Technology on Reliability and Environmental Engineering Laboratory, School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Beijing Aeronautical Science & Technology Research Institute, Commercial Aircraft Corporation of China Ltd., Beijing 102211, China
Author to whom correspondence should be addressed.
Entropy 2019, 21(8), 724;
Received: 25 June 2019 / Revised: 19 July 2019 / Accepted: 23 July 2019 / Published: 25 July 2019
PDF [2901 KB, uploaded 26 July 2019]


Degradation analysis has been widely used in reliability modeling problems of complex systems. A system with complex structure and various functions may have multiple degradation features, and any of them may be a cause of product failure. Typically, these features are not independent of each other, and the dependence of multiple degradation processes in a system cannot be ignored. Therefore, the premise of multivariate degradation modeling is to capture and measure the dependence among multiple features. To address this problem, this paper adopts copula entropy, which is a combination of the copula function and information entropy theory, to measure the dependence among different degradation processes. The copula function was employed to identify the complex dependence structure of performance features, and information entropy theory was used to quantify the degree of dependence. An engineering case was utilized to illustrate the effectiveness of the proposed method. The results show that this method is valid for the dependence measurement of multiple degradation processes. View Full-Text
Keywords: copula entropy; measure; dependence; multiple degradation processes copula entropy; measure; dependence; multiple degradation processes

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Sun, F.; Zhang, W.; Wang, N.; Zhang, W. A Copula Entropy Approach to Dependence Measurement for Multiple Degradation Processes. Entropy 2019, 21, 724.

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