We discuss a statistical framework that underlies envelope detection schemes as well as dynamical models based on Hidden Markov Models (HMM) that can encompass both discrete and continuous sensor measurements for use in Integrated System Health Management (ISHM) applications. The HMM allows for the rapid assimilation, analysis, and discovery of system anomalies. We motivate our work with a discussion of an aviation problem where the identification of anomalous sequences is essential for safety reasons. The data in this application are discrete and continuous sensor measurements and can be dealt with seamlessly using the methods described here to discover anomalous flights. We specifically treat the problem of discovering anomalous features in the time series that may be hidden from the sensor suite and compare those methods to standard envelope detection methods on test data designed to accentuate the differences between the two methods. Identification of these hidden anomalies is crucial to building stable, reusable, and cost-efficient systems. We also discuss a data mining framework for the analysis and discovery of anomalies in high-dimensional time series of sensor measurements that would be found in an ISHM system. We conclude with recommendations that describe the tradeoffs in building an integrated scalable platform for robust anomaly detection in ISHM applications.