Generalized Functional Mixed Models for Accelerated Degradation-Based Reliability Analysis

Abstract

As sensing technology advances, engineers can monitor a system's physical characteristics or performance measures for reliability assessments. The evolution of such measurements as the system deteriorates can be modeled as a collection of multivariate degradation processes. The system is considered failed when any of the degradation processes reaches its predetermined threshold. In practice, degradation data are highly variable due to unobserved environmental factors, unit-specific parameters induced by underlying frailties, and physical deterioration being a function of process covariates, such as load, ambient moisture, and temperature. The later relationships, however, are often approximated through empirical transformations such as the Arrhenius model. However, as the number of degradation processes increases, model flexibility and computational cost increases in standard stochastic process models. In this article, we propose an additive functional mixed effects and Gaussian process model that isolates all sources of uncertainty and provides flexibility to incorporate physics knowledge in the reliability modeling. A comprehensive simulation study and a case study on a tuner's accelerated degradation data are presented to illustrate the capability of the proposed model and statistical methods.