Statistical Modeling and Inference for Lifetime Data in Reliability and Survival Analysis

Abstract

Vast lifetime data arises in reliability and survival fields, which contains the information of the failure mechanism of systems. To capture the contained information and further improve the systems reliability, statistical modeling becomes an efficient tool for the quantitative analysis of lifetime data. As there are various types of lifetime data, our study will mainly focus on the three most common types: failure time data, recurrent failure time data and degradation data. The dissertation is composed of the statistical modelling and inference addressing the worthy studying issues of each of the above types of data.

Failure time data refers to the collection of lifetimes of systems. Due to the limitations of budget, technology and the collection procedures, the data are sometimes censored and truncated. We first concern about the interval-censored failure time data arising from survival analysis in biostatistics. It is of main interest to identify and study the effects of the risk factors. A Bayesian additive Cox model is utilized to describe the relationship between the risk factors and the failure times. This model can achieve parameters estimation and variables selection, which efficiently improves the model interpretability and the predictive ability. An easy to implement Expectation-Maximization algorithm is developed for model fitting using a two-stage data augmentation procedure. The results of simulation experiments and the myocardial infraction data study compared with traditional method lasso further emphasize the efficiency of the proposed method.

In real world clinical settings, the rapidly paced adoption of electronic health records (EHR) allows more information to be collected and made available for analysis, resulting in a large number of patients and longitudinal biomarkers. Assuming that those patients come from a homogeneous population is not able to capture the characteristics of subgroups. A case study based on the records of 194,265 patients diagnosed with type 2 diabetes mellitus (T2DM) from 1955 to 2020 of the SingHealth Diabetes Registry (SDR) is conducted to reveal the relationship between HbA_1c trajectories and the occurrence of recurrent hospitalization for heart failure (HHF). We applied the latent class growth model to HbA_1c trajectories for distinguishing the heterogeneous population. Given the identified latent classes, the recurrent HHF process is modeled by nonhomogeneous Poisson process (NHPP). The mean survival probability of each class can qualitatively explain its association with HbA_1c levels.

In some reliability applications, a system can continue to be in operation after the failure is repaired. The time record of the recurrent failures is called recurrent data. A main challenge in reliability analysis of repairable systems is to model the heterogeneity in their failure behavior, which can be reflected by the corresponding recurrent failure-time data. To capture the system heterogeneity for data analysis, a system-specific frailty (random effect) is typically introduced in most existing statistical models. In practice, the random effect of repairable systems tends to be time-varying; for example, each repair action could change system’s physical properties. Prior studies, however, take no account of this time-varying nature and few of them circumvent the risk of model misspecification on the parametric distribution of frailty. This thesis proposed a semiparametric model that uses multivariate Gaussian convolution processes (MGCPs) to meet the above challenges. We use the trend renewal process to model the baseline intensity function of each repairable system. Based on the baseline intensity function, we then introduce MGCPs to simultaneously factor in heterogeneity and infer commonalities across multiple systems. Simulation studies show the advantages of our model in terms of robustness and estimation accuracy. A group of oil and gas well systems are used to illustrate the application of the proposed model.

Degradation data involves the monitored measurements of some physical characteristics over time that are related to the failure of systems, which provides a large amount of information. Once the degradation reaches a predetermined threshold, the system is usually considered as failure. An important object of degradation modeling is to predict the remaining useful life (RUL) of systems in operation. Efficient detection of anomaly, and therefore the first predicting time (FRT), helps improve RUL prediction through maintenance and repair. In this part, we consider a nonparametric FPT determination method that free from the effect of misspecification error in the health index distribution. Then an RUL prediction method is established based on a modified exponential degradation model. Numerical studies reveal that the proposed method has significant benefits over some existing alternatives.

Date of Award	10 Oct 2023
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Min XIE (Supervisor)