Nonhomogeneous Subordinators and Lévy Copulas for Reliability Analysis of Time-Dependent Degradation Processes

Yu Shi; Qianmei Feng

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arXiv · 2610.17580

Nonhomogeneous Subordinators and Lévy Copulas for Reliability Analysis of Time-Dependent Degradation Processes

Yu Shi·Qianmei Feng

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Abstract

Many systems in engineering applications may experience complex multi-dimensional degradation processes involving random jumps. Analyzing the reliability of such degradation processes presents significant challenges. Previously developed models have utilized multi-dimensional Lévy subordinators and Lévy copulas to describe these processes, with reliability functions expressed through characteristic functions and Laplace transforms (Shu et al., 2015, 2016, Shi et al., 2020, Shi and Feng, 2024). However, these models are restricted to stationary linear paths and homogeneous Lévy subordinators. In real-world scenarios, increments in a degradation process are often time-dependent and nonhomogeneous. To address this limitation of previous studies, this work extends existing degradation models by introducing nonhomogeneous Lévy subordinators, which are designed to capture time-varying complexities inherent in degradation processes. Unlike conventional degradation models that often assume a constant rate of jumps, nonhomogeneous Lévy subordinators aim to provide a more flexible representation of degradation behaviors that evolve under varying external conditions and internal system dynamics. Additionally, the joint behaviors of multiple degradation processes are characterized using Lévy copulas, enabling a more comprehensive analysis of system reliability. Numerical examples are provided to illustrate the applicability of these models in lifetime analysis.

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Yu Shi, Qianmei Feng. 2026-10-13. Nonhomogeneous Subordinators and Lévy Copulas for Reliability Analysis of Time-Dependent Degradation Processes. https://arxiv.org/abs/2610.17580

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