This book introduces a new notion of replacement in maintenance and reliability theory. Replacement Overtime where replacement is done 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 improvements 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 the reader will be introduced to new topics and methods and learn how to apply this knowledge practically 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 useful guide for reliability engineers and managers who have difficulties in maintenance of computer and production systems with random working cycles.