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This book introduces how to do random maintenance. The classical standard age and periodic replacement, preventive maintenance and inspection policies convert to the respective random maintenance policies. Optimum random policies are derived and compared theoretically and numerically with the standard ones. It is shown that they are better than the standard ones in what conditions. Furthermore, random policies are applied to scheduling problems, backup policies of database systems, maintenance policies of cumulative damage models and reliability analysis of redundant systems with random number of units.§§This book is the first book written on random maintenance policies. The reader will learn new topics and techniques and how to apply random policies to actual reliability models. Especially, this book will serve as essential guide to new subject of study for graduate students and researchers. This also would give a useful guide for reliability engineers and managers who have some doubts about usual maintenance and are worried about how to do maintenance of new and large systems.§