Reliability theory is a major concern for engineers and managers engaged in making high quality products and designing highly reliable systems. "Advanced Reliability Models and Maintenance Policies" is a survey of new research topics in reliability theory and optimization techniques in reliability engineering. The book introduces partition and redundant problems within reliability models, and provides optimization techniques. The book also indicates how to perform maintenance in a finite time span and at failure detection, and to apply recovery techniques for computer systems. New themes such as reliability complexity and service reliability in reliability theory are theoretically proposed, and optimization problems in management science using reliability techniques are presented. The book is an essential guide for graduate students and researchers in reliability theory, and a valuable reference for reliability engineers engaged both in maintenance work and in management and computer systems.