Nonhomogeneous Subordinators and Lévy Copulas for Reliability Analysis of Time-Dependent Degradation Processes
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.
Related
- Modeling dependent degradation data considering inherent causal relationships for reliability analysis and remaining useful life prediction
- Reliability and Preventive Maintenance for Multivariate Gamma Degradation with Shared Random Effects and Cumulative Environmental Shock Damage
- The shift paradigm in photovoltaic reliability: A critical review of degradation
- Comparing the reliability of coherent systems with heterogeneous, dependent and distribution-free components
- Time-reliability optimization of multi-pass underfill dispensing sequences on printed circuit boards: a schedule-dependent reliability model solved by a multiset-permutation binary-addition-tree algorithm
BibTeX
@misc{shi2026nonhomogeneous,
title = {{Nonhomogeneous Subordinators and Lévy Copulas for Reliability Analysis of Time-Dependent Degradation Processes}},
author = {Yu Shi and Qianmei Feng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17580},
eprint = {2610.17580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17580},
}
RIS
TY - UNPB
TI - Nonhomogeneous Subordinators and Lévy Copulas for Reliability Analysis of Time-Dependent Degradation Processes
AU - Yu Shi
AU - Qianmei Feng
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17580
UR - https://arxiv.org/abs/2610.17580
AB - 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.
ER -