Due to advances in technology, operational data can now be collected automatically by industries, and organizations are accumulating enormous volumes of data. There is a growing demand for methods of extracting useful knowledge to assist in strategic decision making and provide competitive advantages. In particular, the ability to predict exactly when and how a particular component of a system will break down not only reduces inspection costs, downtime and spare-parts inventories, but enables organizations to schedule maintenance dynamically. Recent research on prognostics and health management (PHM) has emphasized the collection and analysis of online data to assess and predict the condition of individual components or systems and thereby improve reliability and safety. On the other hand, recently developed methods of data modeling, such as data-mining algorithms, have provided a wide spectrum of alternative techniques for identifying patterns in data. The aim of this project is to facilitate the use of data-mining methods to predict the health conditions of components/systems. In this study, a bottom-up approach to system-health diagnostics and prognostics is taken by first addressing problems at the component level. Emphasis is placed on the application of statistical data-mining techniques to sensor-based time series data. The significance and contributions of the thesis are outlined in the following. An empirical procedure with a naive Bayes (NB) classifier is shown to provide robust RUL prediction over time for Li-ion batteries under different operating conditions. Using Li-ion battery capacity depletion data, the prediction performance of the NB procedure is shown to be more stable and competitive than that of an SVM, despite its combined modeling of batteries under different operating conditions. We used the same procedure to predict the RUL of bearings with incipient outer race defects. The study introduces a bearing-diagnostic technique based on one-versus-all (OVA) class binarization, with a focus on multiple defects that may occur concurrently. As shown using two bearing-vibration datasets, the OVA technique has the potential to improve the accuracy of fault diagnosis at the same time allows concurrent-defect diagnosis from normal and single-defect training data. The proposed technique is evaluated using an SVM and a C4.5 decision tree, two popular classification algorithms with widespread application in system-health diagnostics and prognostics. A distance-based analytical model of dynamical systems reconstructed through time-delay embedding is proposed for the detection and comparison of the dynamical structure of bearings for fault diagnostics. The earth mover's distance (EMD), a Wasserstein distance metric, is used to compare dynamical systems reconstructed from bearing-vibration data, with a baseline reconstructed from normal bearing data. This enables the construction of a severity index over time. Multi-dimensional scaling (MDS) is used to visualize the EMDs of different reconstructed dynamical systems in a two-dimensional space for fault-type assessment. The proposed method is evaluated using simulated and laboratory data on bearings. In this thesis, three data-driven methods are proposed for solving two kinds of problems. The first method entailed the use of capacity-degradation data to predict the RUL of a Li-ion battery. The second and third methods involved the use of vibration data to diagnose bearing defects after incipient faults. In the latter problem, both the diagnostic results at a specific time of operation and the trend of degradation were considered. Common mechanical (bearings) and electrical (batteries) components were studied. Both simulated data and laboratory experimental data were used to demonstrate the proposed methods.