Reliability analysis for binary Lévy degradation processes using characteristic functions

Abstract

AbstractMany engineering systems experience complex degradation processes along with random shocks that often pose a risk to the safe and reliable operations of the system. The analysis of dependence among multiple degradation processes has been a challenging task in the field of reliability engineering. To study dependence behaviors and jump uncertainties among degradation processes, one of the effective approaches is to model these degradation processes using multidimensional Lévy subordinators. However, a critical obstacle arises in determining the convergent mathematical form of the reliability function under Lévy measures and distributions. To obtain a closed form of reliability function, this study investigates the Lévy measure and the characteristic function of multiple dependent degradation processes. Each degradation process is modeled by a one‐dimensional Lévy subordinator utilizing the marginal Lévy measure and characteristic function. The dependence among all dimensions is described by the Lévy copula and the associated multidimensional Lévy measure. For a two‐dimensional case, we derive the reliability function and probability density function (PDF) from the characteristic function and the inverse Fourier transform. Numerical examples are provided to demonstrate the proposed models for reliability and lifetime analysis of multidimensional degradation processes in engineering systems.