The Universal Generating Function in Reliability Analysis and Optimization
Many real-world systems in engineering are composed of multi-state components that have different performance levels and several failure modes. These have effects on the entire system’s performance. Most books on reliability theory are devoted to traditio
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Series Editor Professor Hoang Pham Department of Industrial Engineering Rutgers The State University of New Jersey 96 Frelinghuysen Road Piscataway, NJ 08854-8018 USA
Other titles in this series Warranty Management and Product Manufacture D.N.P. Murthy and W. Blischke Maintenance Theory of Reliability T. Nakagawa Publication due August 2005
Gregory Levitin
The Universal Generating Function in Reliability Analysis and Optimization With 142 Figures
Gregory Levitin, PhD The Israel Electric Corporation Ltd, P.O.B. 10, Haifa 31000, Israel
British Library Cataloguing in Publication Data Levitin, Gregory Universal generating function in reliability analysis and optimization. — (Springer series in reliability engineering) 1. Reliability (Engineering) — Mathematical models I. Title 620′.00452′015118 ISBN 1852339276 Library of Congress Control Number: 2005923752 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Springer Series in Reliability Engineering ISSN 1614-7839 ISBN-10: 1-85233-927-6 ISBN-13: 978-1-85233-927-2 Springer Science+Business Media springeronline.com © Springer-Verlag London Limited 2005 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera-ready by author Printed in the United States of America (TB/IBT) 69/3830-543210 Printed on acid-free paper
To Victor Levitin
Preface
Most books on reliability theory are devoted to traditional binary reliability models allowing only two possible states for a system and its components: perfect functionality and complete failure. Many real-world systems are composed of multi-state components, which have different performance levels and several failure modes with various effects on the system’s entire performance. Such systems are called multi-state systems (MSSs). Examples of MSSs are power systems or computer systems where the component performance is respectively characterized by the generating capacity or the data processing speed. For MSSs, the outage effect will be essentially different for units with different performance rates. Therefore, the reliability analysis of MSSs is much more complex when compared with binary-state systems. In real-world problems of MSS reliabi
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