Computing and updating the first-passage time distribution for randomly evolving degradation signals

This article considers systems that degrade gradually and whose degradation can be monitored using sensor technology. Different degradation modeling techniques, such as the Brownian motion process, gamma process, and random coefficients models, have been used to model the evolution of sensor-based degradation signals with the goal of estimating lifetime distributions of various engineering systems. A parametric stochastic degradation modeling approach to estimate the Residual Life Distributions (RLDs) of systems/components that are operating in the field is presented. The proposed methodology rests on the idea of utilizing in situ degradations signals, communicated from fielded components, to update their respective RLDs in real time. Given the observed partial degradation signals, RLDs are evaluated based on a first-passage time approach. Expressions for the first-passage time for a base case linear degradation model, in which the degradation signal evolves as a Brownian motion, are derived. The model is tested using simulated and real-world degradation signals from a rotating machinery application.