Statistical Methods for Multivariate Functional Data Clustering, Recurrent Event Prediction, and Accelerated Degradation Data Analysis

Abstract

In this dissertation, we introduce three projects in machine learning and reliability applications after the general introductions in Chapter 1. The first project concentrates on the multivariate sensory data, the second project is related to the bivariate recurrent process, and the third project introduces thermal index (TI) estimation in accelerated destructive degradation test (ADDT) data, in which an R package is developed. All three projects are related to and can be used to solve certain reliability problems. Specifically, in Chapter 2, we introduce a clustering method for multivariate functional data. In order to cluster the customized events extracted from multivariate functional data, we apply the functional principal component analysis (FPCA), and use a model based clustering method on a transformed matrix. A penalty term is imposed on the likelihood so that variable selection is performed automatically. In Chapter 3, we propose a covariate-adjusted model to predict next event in a bivariate recurrent event system. Inspired by geyser eruptions in Yellowstone National Park, we consider two event types and model their event gap time relationship. External systematic conditions are taken account into the model with covariates. The proposed covariate adjusted recurrent process (CARP) model is applied to the Yellowstone National Park geyser data. In Chapter 4, we compare estimation methods for TI. In ADDT, TI is an important index indicating the reliability of materials, when the accelerating variable is temperature. Three methods are introduced in TI estimations, which are least-squares method, parametric model and semi-parametric model. An R package is implemented for all three methods. Applications of R functions are introduced in Chapter 5 with publicly available ADDT datasets. Chapter 6 includes conclusions and areas for future works.