This book introduces a new concept of replacement in maintenance and reliability theory. Replacement overtime, where replacement occurs at the first completion of a working cycle over a planned time, is a new research topic in maintenance theory and also serves to provide a fresh optimization technique in reliability engineering. In comparing replacement overtime with standard and random replacement techniques theoretically and numerically, 'Maintenance Overtime Policies in Reliability Theory' highlights the key benefits to be gained by adopting this new approach and shows how they can be applied to inspection policies, parallel systems and cumulative damage models. Utilizing the latest research in replacement overtime by internationally recognized experts, readers are introduced to new topics and methods, and learn how to practically apply this knowledge to actual reliability models. This book will serve as an essential guide to a new subject of study for graduate students and researchers and also provides a valuable resource for reliability engineers and managers who have difficulties maintaining computer and production systems with random working cycles.