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The analysis of multiple dependent degradation processes is a challenging research work in the reliability field, especially for complex degradation with random jumps. To integrally handle the jump uncertainties in degradation and the dependence among degradation processes, we construct multi-dimensional Lévy processes to describe multiple dependent degradation processes in engineering systems. The evolution of each degradation process can be modeled by a one-dimensional Lévy subordinator with a marginal Lévy measure, and the dependence among all dimensions can be described by Lévy copulas and the associated multiple-dimensional Lévy measure. This Lévy measure is obtained from all its one-dimensional marginal Lévy measures and the Lévy copula. We develop the Fokker-Planck equations to describe the probability density in stochastic systems. The Laplace transforms of both reliability function and lifetime moments are derived. Numerical examples are used to demonstrate our models in lifetime analysis.