Abstract
Modern society increasingly depends on engineered systems in diverse fields such as defense, communication, and healthcare. Both the reliability and maintainability of these systems is therefore paramount. Past research had developed models to identify optimal periodic maintenance policies such as those that minimize cost or maximize availability. However, these maintenance policies may be suboptimal when the components of a system are subject to correlated or dependent failure. Moreover, the vast majority of past research on correlated and dependent failure is focused on positive correlation and dependence, yet negative correlation and dependence are also important to the design of resilient systems. To address these limitations, this dissertation makes several modeling and methodological contributions in the context of a variety of system and software reliability and maintenance contexts, including binary state systems, consecutive k-out-of-n: failed systems composed of multi-state components, and a software computation subject to checkpointing operations. Primary contribution include: (i) models and method to quantify the impact of correlated failures on maintenance models in order to identify optimal maintenance intervals despite correlated failures and (ii) efficient methods to obtain algebraic expressions with explicit correlation parameters as well as exact numerical methods for the reliability of systems composed of non-identical components and arbitrary combinations of non-identical positive and negative correlations between the failures of the components.