Time series chain graph for modelling reliability covariates in degradation process

Abstract

In reliability models, covariate is synonymous with risk factors. These factors potentially contribute to the failure rate change throughout product lifetime. The task of reliability covariate model is to evaluate the mathematical relationship between a set of risk factors and the failure mechanism. The traditional non-parametric proportional hazard model based analysis are unable to specify the degradation paths or the distributions of failure measurements, and the semi-parametric models such as logistic regression model assume a specific distribution to model the entire degradation process and are unable to accommodate variation. Therefore, a general model considering the conditional association of covariates with survival outcome and association between covariates is necessary. Probabilistic graphical models allow to describe and manipulate conditional independence relations between variables in multivariate data. Time series chain graph, as one of the most recently developed probabilistic graphical models, provides a structure to incorporate the covariates and the degradation status measurements changing over time. The study in this dissertation is the first attempt to apply time series chain graph in analyzing reliability covariate model, in which the dependencies between system operating factors and performance measurements as well as time are explicitly described. The construction of time series chain graph in reliability covariate model for discrete data, continuous data, and mixed discrete and continuous data, with algorithms of model selection and parameter estimation, are proposed respectively. In the time series chain graphical reliability covariate model with discrete variables, the graph structure is trained by the observations through EH-procedure, and the goodness-of-fit tests for sparse data set are embedded in the algorithm to accommodate the greatly increased number of variables as time accumulates compared to the number of observations. In the model with continuous or mixed variables, the Gaussian copula is used to relax the assumption of multivariate normally distributed dataset, and the dependencies incorporated in the graph parameters are modeled by the transformed latent Gaussian variables. The validity of the proposed model is illustrated by a simulated turbofan engine degradation case study, which consists of time series for engine operation and degradation process. The data set is for estimating the engine remaining useful life, therefore, the method of using time series chain graph in degradation prediction is proposed.