Reliability analysis plays an important role in keeping manufacturers in a competitive position. It can be applied in many areas such as warranty predictions, maintenance scheduling, spare parts provisioning, and risk assessment. This dissertation focuses on statistical modeling and predictions based on lifetime data, degradation data, and recurrent event data. The datasets used in this dissertation come from the field, and have complicated structures. The dissertation consists of three main chapters, in addition to Chapter 1 which is the introduction chapter, and Chapter 5 which is the general conclusion chapter. Chapter 2 consists of the traditional time-to-failure data analysis. We propose a statistical method to address the failure data from an appliance used at home with the consideration of retirement times and delayed reporting time. We also develop a prediction method based on the proposed model. Using the information of retirement-time distribution and delayed reporting time, the predictions are more accurate and useful in the decision making. In Chapter 3, we introduce a nonlinear mixed-effects general path model to incorporate dynamic covariates into degradation data analysis. Dynamic covariates include time-varying environmental variables and usage condition. The shapes of the effect functions of covariates may be constrained to be, for example, monotonically increasing (i.e., higher temperature is likely to cause more damage). Incorporating dynamic covariates with shape restrictions is challenging. A modified alternative algorithm and the corresponding prediction method are proposed. In Chapter 4, we introduce a multi-level trend-renewal process (MTRP) model to describe component-level events in multi-level repairable systems. In particular, we consider two-level repairable systems in which events can occur at the subsystem level, or the component (within the subsystem) level. The main goal is to develop a method for estimation of model parameters and a procedure for prediction of the future replacement events at component level with the consideration of the effects from the subsystem replacement events. To explain unit-to-unit variability, time-dependent covariates as well as random effects are introduced into the heterogeneous MTRP model (HMTRP). A Metropolis-within-Gibbs algorithm is used to estimate the unknown parameters in the HMTRP model. The proposed method is illustrated by a simulated dataset. / Ph. D.

This dissertation aims to develop methods for statistical predictions based on various types of data from different areas. We focus on applications from reliability and spatial epidemiology. Chapter 1 gives a general introduction of statistical predictions. Chapters 2 and 3 investigate the photodegradation of an organic coating, which is mainly caused by ultraviolet (UV) radiation but also affected by environmental factors, including temperature and humidity. In Chapter 2, we identify a physically motivated nonlinear mixed-effects model, including the effects of environmental variables, to describe the degradation path. Unit-to-unit variabilities are modeled as random effects. The maximum likelihood approach is used to estimate parameters based on the accelerated test data from laboratory. The developed model is then extended to allow for time-varying covariates and is used to predict outdoor degradation where the explanatory variables are time-varying. Chapter 3 introduces a class of models for analyzing degradation data with dynamic covariate information. We use a general path model with random effects to describe the degradation paths and a vector time series model to describe the covariate process. Shape restricted splines are used to estimate the effects of dynamic covariates on the degradation process. The unknown parameters of these models are estimated by using the maximum likelihood method. Algorithms for computing the estimated lifetime distribution are also described. The proposed methods are applied to predict the photodegradation path of an organic coating in a complicated dynamic environment. Chapter 4 investigates the Lyme disease emergency in Virginia at census tract level. Based on areal (census tract level) count data of Lyme disease cases in Virginia from 1998 to 2011, we analyze the spatial patterns of the disease using statistical smoothing techniques. We also use the space and space-time scan statistics to reveal the presence of clusters in the spatial and spatial/temporal distribution of Lyme disease. Chapter 5 builds a predictive model for Lyme disease based on historical data and environmental/demographical information of each census tract. We propose a Divide-Recombine method to take advantage of parallel computing. We compare prediction results through simulation studies, which show our method can provide comparable fitting and predicting accuracy but can achieve much more computational efficiency. We also apply the proposed method to analyze Virginia Lyme disease spatio-temporal data. Our method makes large-scale spatio-temporal predictions possible. Chapter 6 gives a general review on the contributions of this dissertation, and discusses directions for future research. / Ph. D.