Background: Many failures of engineering structures and equipment are attributed to the failure of a single component. It is of great importance to identify those critical components and understand how components' criticality changes over time under dynamic environments. Objective: In this paper, we investigate the criticality analysis for components with multi-dimensional degradation under time-varying environmental conditions. Methods: The component degradation is modeled as a k-dimensional Wiener process and a component fails when any of the k degradation processes attains a threshold level. Results: Since the degradation process is often influenced by the environmental conditions, we assume that both the mean and diffusion of the degradation process are time-dependent functions for a given environmental profile, which evolves either deterministically or stochastically. Conclusions: We derive expression for the criticality measure of the component with time, illustrate the analysis of component criticality under time-varying environmental conditions and demonstrate the necessity to consider the change of environmental conditions in analyzing component criticality.


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