Nonlinear Stochastic Modeling with Heterogeneous Covariates for Degradation Analysis Applied to Wax Lubrication Layer

Wax is a commonly used lubricant in many applications. To ensure its security and dependability, degradation analyses for creep are typically conducted. However, challenges arise due to the poorly understood inherent mechanisms of wax and the complicated experimental environment required, leading to nonlinear trends and heterogeneous covariates. In such cases, traditional methods based on parametric forms or linear assumptions may lack the flexibility to capture the complexities and randomness of the degradation process effectively. To address these challenges, we propose a comprehensive degradation analysis framework that employs a Wiener process with an unspecified mean function. By eliminating parametric forms, this approach offers a more versatile way to model nonlinear degradation trends. Moreover, it treats environmental covariates as random variables to handle random environmental influences. We develop tailored semiparametric estimators for the model and establish theoretical asymptotic results that guarantee the consistency and convergence of the proposed estimators. A series of numerical experiments are conducted to illustrate the performance of the estimators and validate their convergence properties. The method is applied to a wax lubrication layer, demonstrating its efficacy in analyzing nonlinear degradation data in a random working environment. This work advances the understanding of wax degradation mechanisms and provides a flexible tool for degradation analysis in materials with heterogenic environments and poorly understood behaviors.