Criticality measures for components with multi-dimensional degradation

Abstract

Failures of engineering structures and equipment are often attributed to the failure of a single component. Hence, it is important to identify critical components in a system and understand how a component's criticality changes over time under dynamic environments. This article investigates the criticality analysis for components with multiple competing failure modes due to degradation. The component degradation is modeled as a k-dimensional Wiener process. A component fails when any of the k degradation processes associated with that component attains a certain threshold level. Motivated by Nelson's cumulative exposure model, a relationship between both the mean and diffusion of the degradation process and environmental conditions is established. Expressions of a component's criticality measures are derived. Numerical examples are presented to illustrate the criticality analysis.