Multivariate Degradation Modeling of Smart Electricity Meter with Multiple Performance Characteristics via Vine Copulas

Abstract

For smart electricity meter with multiple performance characteristics (PCs) with coupling relationships because of amounts of components experiencing multiple deteriorating processes, we develop a multivariate degradation modeling method via vine copulas to estimate the reliability of products with multiple PCs reflecting degradation states. In the multivariate model, pair-copula construction and vine graphical representation are used to describe the mutual relationship among PCs to overcome the lack of multivariate copula in high-dimensional cases. Each PC model of smart electricity meter is built by using drift Brownian motion to describe degradation processes of each PC on the basis of degradation mechanism analysis, and parameters are estimated by using likelihood estimation method. The Pearson correlation coefficient, Kendall's τ and product information are used to analyze correlation among those PCs. Furthermore, on the basis of conditional probability theory, the vine graph is used to construct a multivariate copula which can be decomposed into pair copulas. Akaike information criterion principle is utilized to choose the forms of pair-copula functions in the correlation model. Finally, the reliability joint distribution of all PCs of smart electricity meter is obtained with combining all PCs' marginal distributions and copula functions. Copyright © 2016 John Wiley & Sons, Ltd.