Statistical Modeling for Spatio-Temporal Degradation Data

TL;DR

This paper develops a comprehensive statistical model for spatio-temporal degradation data, capturing complex spatial and temporal dependencies, heterogeneity, and propagation, with applications demonstrated through a numerical example.

Contribution

It introduces a novel stochastic modeling framework that accounts for spatial heterogeneity, anisotropic covariance, and degradation propagation, linking to physical degradation processes.

Findings

Model captures complex spatio-temporal dependencies

Special cases include pure time-dependent models

Connection to physical degradation processes established

Abstract

This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation models, a special random field is constructed for modeling the spatio-temporal degradation process. In particular, we express the degradation at any spatial location and time as an additive superposition of two stochastic components: a dynamic spatial degradation generation process, and a spatio-temporal degradation propagation process. Some unique challenges are addressed, including the spatial heterogeneity of the degradation process, the spatial propagation of degradation to neighboring areas, the anisotropic and space-time non-separable covariance structure often associated with a complex spatio-temporal degradation process, and the computational issue related to parameter estimation. When the spatial dependence is ignored, we show that the proposed spatio-temporal degradation model incorporates some existing pure time-dependent degradation processes as its special cases. We also show the connection, under special conditions, between the proposed model and general physical degradation processes which are often defined by stochastic partial differential equations. A numerical example is presented to illustrate the modeling approach and model validation.