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Springer Series in Reliability Engineering
Series EditorHoang Pham
For further volumes:http://www.springer.com/series/6917
Anatoly Lisnianski • Ilia FrenkelEditors
Recent Advances in SystemReliability
Signatures, Multi-state Systemsand Statistical Inference
123
Dr. Anatoly LisnianskiPlanning, Development and Technology
Division,The System Reliability DepartmentThe Israel Electric Corporation LtdNew Office Building, st. Nativ haor, 1P.O. Box 10HaifaIsraele-mail: [email protected];[email protected]
Dr. Ilia FrenkelIndustrial Engineering and Management
Department,Center for Reliability and Risk
ManagementShamoon College of EngineeringBialik/Basel Sts.84100 Beer ShevaIsraele-mail: [email protected]
ISSN 1614-7839ISBN 978-1-4471-2206-7 e-ISBN 978-1-4471-2207-4DOI 10.1007/978-1-4471-2207-4Springer London Dordrecht Heidelberg New York
British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library
Library of Congress Control Number: 2011938587
� Springer-Verlag London Limited 2012MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks orregistered trademarks of their respective holders.Apart from any fair dealing for the purposes of research or private study, or criticism or review, aspermitted 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 thepublishers, or in the case of reprographic reproduction in accordance with the terms of licenses issuedby the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should besent to the publishers.The use of registered names, trademarks, etc., in this publication does not imply, even in the absence ofa specific statement, that such names are exempt from the relevant laws and regulations and thereforefree for general use.The publisher makes no representation, express or implied, with regard to the accuracy of the infor-mation contained in this book and cannot accept any legal responsibility or liability for any errors oromissions that may be made.
Cover design: eStudio Calamar, Berlin/Figueres
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
The book is in the honor of Prof. IlyaGertsbakh and Prof. Igor Ushakov, who havemade a great pioneering contribution to allareas of reliability and, in particular, to thetopics of signatures and multi-state systems.
Preface
This book covers the recent developments in modern reliability theory, mainly insuch important areas as signatures and multi-state systems and their influence onstatistical inference. Research in these areas is growing rapidly due to manysuccessful applications in very diverse problems. As the result, many industrieshave benefited from adopting the corresponding methods.
These methods have attracted increasing attention in recent years for solvingmany complex problems which were inspired by nature and technology. Newmethods have been successfully applied to solving many complex problems wheretraditional problem-solving methods have failed.
This book presents new theoretical issues that were not previously presented inthe literature, as well as the solutions of important practical problems and casestudies illustrating the application methodology.
The book provides an overview of the recent developments in the theory ofsignatures and demonstrates their role in the study of dynamic reliability andnonparametric inference for lifetime distribution of monotone systems. Newproperties of system signatures (D-spectra) and component importance D-spectrahave been investigated. It was demonstrated how component Birnbaum impor-tance measures can be expressed via these spectra and how bounds on lifetimevariances for coherent and mixed systems can be found by using signatures. Inaddition, it was pointed out on the connection between several aspects of proba-bility-signature and structure-signature.
Concerning multi-state system (MSS) reliability, the book introduces a specialtransform for a discrete-states continuous-time Markov process, so-called LZ-transform and demonstrates the benefits of its applications. In MSS context, thereissues such as practical availability modeling, a case-study for supermarketrefrigerating system, finding optimal reserve structure for power generating sys-tem, determination of vital activities in reliability program, optimal incompletemaintenance, optimal multi-objective reliability allocation, importance analysisbased on multiple-valued logic methods, and optimal replacement and protectionstrategy were also considered. A separate chapter is devoted to the novel issue ofcontinuous-state system reliability. Absorbing controllable Markov processes were
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considered as the models of aging and degradation for some technical and/orbiological objects, as well as a semi-Markov model of MSS operation reliability.
The book aims to be repository for modern theoretical methods and theirapplications in real-world reliability analysis and optimization. Recent advances instatistical inference are presented in this volume by reliability analysis of redun-dant systems with unimodal hazard rate functions, nonparametric estimation ofmarginal temporal functionals, frailty models in survival analysis and reliability,goodness of fit tests for reliability modeling and nonparametric estimators of thetransition probabilities for three-state Markov model.
All chapters are written by leading experts in the corresponding areas. Thisbook will be useful to postgraduate and doctoral students, researchers, reliabilitypractitioners, engineers and industrial managers with interest in reliability theoryand its applications.
We wish to thank all the authors for their insights and excellent contributions tothis book. We would like to acknowledge the assistance of all involved in thereview process of the book, without whose support this book could not have beensuccessfully completed. We want to thank all who participated in the reviewingprocess: Prof. Somnath Datta, University of Louisville, USA, Prof. Ilya Gertsbakh,Ben Gurion University of the Negev, Israel, Dr. Gregory Gurevich, SCE–ShamoonCollege of Engineering, Israel, Prof. Alex Karagrigoriou, University of Cyprus,Cyprus, Prof. Ron S. Kenett, KPA Ltd., Israel, Dr. Edward Korczak, Telecom-munications Research Institute, Poland, Prof. Michael Peht, University of Mary-land, USA, Prof. Dmitrii Silvestrov, Stockholm University, Sweden, Dr. ArmenStepanyants, Institute of Control Science, RAS, Russia, Prof. Guram Tsitsiashvili,Institute for Applied Mathematics, Eastern Branch of RAS, Russia, Dr. ValentinaVictorova, Institute of Control Science, RAS, Russia, Prof. Ilia Vonta, NationalTechnical University of Athens, Greece, Prof. David Zucker, Hebrew Universityof Jerusalem, Israel.
We would like to express our sincere appreciation to Prof. Ilya Gertsbakh fromBen-Gurion University, Israel, for his great impact on book preparation.
We would like also to thank the SCE–Shamoon College of Engineering (Israel),and its president, Prof. Jehuda Haddad and the SCE Industrial Engineering andManagement Department and its dean Prof. Zohar Laslo for their support and everpresent help at all stages of the work.
Our special thanks to Boris Frenkel from Kivitek Ltd. (Israel) for his technicalassistance and help.
It was indeed our pleasure working with the Springer Senior Editorial Assistant,Ms. Claire Protherough.
Israel, May 2011 Anatoly LisnianskiIlia Frenkel
viii Preface
Contents
1 Signature Representation and Preservation Results forEngineered Systems and Applications to Statistical Inference . . . . 1N. Balakrishnan, Jorge Navarro and Francisco J. Samaniego
2 Using D-Spectra in Network Monte Carlo: Estimationof System Reliability and Component Importance . . . . . . . . . . . . 23Ilya B. Gertsbakh and Yoseph Shpungin
3 Signatures and Symmetry Properties of Coherent Systems. . . . . . 33Fabio Spizzichino and Jorge Navarro
4 Multidimensional Spectra of Multistate Systemswith Binary Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Ilya Gertsbakh and Yoseph Shpungin
5 Applications of Samaniego Signatures to Bounds on Variancesof Coherent and Mixed System Lifetimes . . . . . . . . . . . . . . . . . . 63Tomasz Rychlik
6 Lz-Transform for a Discrete-State Continuous-Time MarkovProcess and its Applications to Multi-State System Reliability . . . 79Anatoly Lisnianski
7 Reliability Decisions for Supermarket Refrigeration Systemby using Combined Stochastic Process and Universal GeneratingFunction Method: Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Ilia Frenkel and Lev Khvatskin
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8 Importance Analysis of a Multi-State System Basedon Multiple-Valued Logic Methods . . . . . . . . . . . . . . . . . . . . . . . 113Elena Zaitseva
9 Optimal Replacement and Protection Strategyfor Parallel Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Rui Peng, Gregory Levitin, Min Xie and Szu Hui Ng
10 Heuristic Optimization Techniques for DeterminingOptimal Reserve Structure of Power Generating Systems . . . . . . 145Yi Ding, Lalit Goel, Peng Wang, Yuanzhang Sun,Poh Chiang Loh and Qiuwei Wu
11 Determination of Vital Activities in Reliability Programfor Multi-State System by Using House of Reliability. . . . . . . . . . 155Shuki Dror and Kobi Tsuri
12 Multi-State Availability Modeling in Practice . . . . . . . . . . . . . . . 165Kishor S. Trivedi, Dong Seong Kim and Xiaoyan Yin
13 Recent Results in the Analysis of Redundant Systems . . . . . . . . . 181Mikhail Nikulin, Noureddine Saaidia and Ramzan Tahir
14 Multiobjective Reliability Allocation in Multi-State Systems:Decision Making by Visualization and Analysisof Pareto Fronts and Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195Enrico Zio and Roberta Bazzo
15 Optimal Incomplete Maintenance in Multi-State Systems. . . . . . . 209Waltraud Kahle
16 Nonparametric Estimation of Marginal Temporal Functionalsin a Multi-State Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219Somnath Datta and A. Nicole Ferguson
17 Frailty or Transformation Models in Survival Analysisand Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237Filia Vonta
18 Goodness-of-Fit Tests for Reliability Modeling . . . . . . . . . . . . . . 253Alex Karagrigoriou
x Contents
19 On the Markov Three-State Progressive Model . . . . . . . . . . . . . . 269Jacobo de Uña-Álvarez
20 Multi-State Semi-Markov Model of the Operation Reliability. . . . 283Franciszek Grabski
21 Reliability of Continuous-State Systems in Viewof Heavy-Tailed Distributed Performance Features . . . . . . . . . . . 295Emil Bashkansky and Tamar Gadrich
22 On Optimal Control of Systems on Their Life Time . . . . . . . . . . 307Vladimir Rykov and Dmitry Efrosinin
Contents xi
Contributors
N. Balakrishnan Department of Mathematics and Statistics, McMaster Univer-sity, Hamilton, Canada, e-mail: [email protected]
Emil Bashkansky Department of Industrial Engineering and Management, OrtBraude College, Karmiel, Israel, e-mail: [email protected]
Roberta Bazzo Dipartimento di Energia, Politecnico di Milano, Milan, Italy,e-mail: [email protected]
Somnath Datta Department of Bioinformatics and Biostatistics, University ofLouisville, Louisville, KY, USA, e-mail: [email protected]
Jacobo deUña-Álvarez Department of Statistics and OR, Facultad de CC Econó-micas y Empresariales, Universidad de Vigo, Vigo, Spain, e-mail: [email protected]
Yi Ding Department of Electrical Engineering, Centre for Electric Technology,Technical University of Denmark, Lyngby, Denmark, e-mail: [email protected]
Shuki Dror Department of Industrial Engineering and Management, Ort BraudeCollege, Karmiel, Israel, e-mail: [email protected]
Dmitry Efrosinin Institut for Stochastic, Johannes Kepler University of Linz,Linz, Austria, e-mail: [email protected]
A. Nicole Ferguson Department of Bioinformatics and Biostatistics, University ofLouisville, Louisville, KY, USA, e-mail: [email protected]
Ilia Frenkel Industrial Engineering and Management Department, Center forReliability and Risk Management, Sami Shamoon College of Engineering, BeerSheva, Israel, e-mail: [email protected]
Tamar Gadrich Department of Industrial Engineering and Management, OrtBraude College, Karmiel, Israel, e-mail: [email protected]
Ilya Gertsbakh Department of Mathematics, Ben Gurion University of the Negev,Beer Sheva, Israel, e-mail: [email protected]
xiii
Lalit Goel Division of Power Engineering, School of Electrical and ElectronicEngineering College of Engineering, Nanyang Technological University, Singa-pore, Singapore, e-mail: [email protected]
Franciszek Grabski Department of Mathematics and Physics, Polish NavalUniversity, Gdynia, Poland, e-mail: [email protected]
Waltraud Kahle Institute of Mathematical Stochastics, Otto-von-Guericke-University, Magdeburg, Germany, e-mail: [email protected]
Alex Karagrigoriou Department of Mathematics and Statisrics, University ofCyprus, Nicosia, Cyprus, e-mail: [email protected]
Lev Khvatskin Industrial Engineering and Management Department, Center forReliability and Risk Management, Sami Shamoon College of Engineering, BeerSheva, Israel, e-mail: [email protected]
Dong Seong Kim Department of Electrical and Computer Engineering, DukeUniversity, Durham, NC, 27708, USA, e-mail: [email protected]
Gregory Levitin, The Israel Electric Corporation Ltd, Haifa, Israel, e-mail:[email protected]
Anatoly Lisnianski The Israel Electric Corporation Ltd, Haifa, Israel, e-mail:[email protected] e-mail: [email protected]
Poh Chiang Loh Division of Power Engineering, School of Electrical and Elec-tronic Engineering College of Engineering, Nanyang Technological University,Singapore, Singapore, e-mail: [email protected]
Jorge Navarro Facultad de Matemáticas, Universidad de Murcia, Murcia, Spain,e-mail: [email protected]
Szu Hui Ng Department of Industrial and Systems Engineering, NationalUniversity of Singapore, Kent Ridge Crescent, Singapore, 119260, Singapore,e-mail: [email protected]
Mikhail Nikulin IMB, Université Victor Segalen Bordeaux 2, Bordeaux 2,France, e-mail: [email protected]
Rui Peng Department of Industrial and Systems Engineering, National Universityof Singapore, Kent Ridge Crescent, Singapore, 119260, Singapore, e-mail:[email protected]
Tomasz Rychlik Institute of Mathematics, Polish Academy of Sciences, Chopina12, Torun, 87100, Poland, e-mail: [email protected]
Vladimir Rykov Department of Applied Mathematics and Computer Modeling,Russian State University of Oil and Gas, Moscow, Russia, e-mail: [email protected]
xiv Contributors
Noureddine Saaidia IMB, Université Victor Segalen Bordeaux 2, Bordeaux 2,France, e-mail: [email protected]; Université Badji Mokhtar,Annaba, Algérie, e-mail: [email protected]
Francisco J. Samaniego Department of Statistics, University of California, Davis,USA, e-mail: [email protected]
Yoseph Shpungin Software Engineering Department, Sami Shamoon College ofEngineering, Beer Sheva, Israel, e-mail: [email protected]
Fabio Spizzichino Department of Mathematics, Università La Sapienza, Rome,Italy, e-mail: [email protected]
Yuanzhang Sun School of Electrical Engineering, Wuhan University, Wuhan,P.R. China, e-mail: [email protected]
Ramzan Tahir IMB, Université Victor Segalen Bordeaux 2, Bordeaux 2, France,e-mail: [email protected]
Kishor S. Trivedi Department of Electrical and Computer Engineering, DukeUniversity, Durham, NC, 27708, USA, e-mail: [email protected]
Kobi Tsuri Department of Industrial Engineering and Management, Ort BraudeCollege, Karmiel, Israel, e-mail: [email protected]
Filia Vonta Department of Mathematics, School of Applied Mathematical andPhysical Sciences, National Technical University of Athens, Athens, Greece, e-mail:[email protected]
Peng Wang Division of Power Engineering, School of Electrical and ElectronicEngineering College of Engineering, Nanyang Technological University, Singa-pore, Singapore, e-mail: [email protected]
Qiuwei Wu Department of Electrical Engineering, Centre for Electric Technol-ogy, Technical University of Denmark, Lyngby, Denmark, e-mail:[email protected]
Min Xie Department of Industrial and Systems Engineering, National Universityof Singapore, Kent Ridge Crescent, Singapore, 119260, Singapore, e-mail:[email protected]
Xiaoyan Yin Department of Electrical and Computer Engineering, Duke Uni-versity, Durham, NC, 27708, USA, e-mail: [email protected]
Elena Zaitseva Department of Informatics, Faculty of Management Science andInformatics, University of Zilina, Zilina, Slovakia, e-mail: [email protected]
E. Zio Chair ‘‘Systems Science and Energetic Challenge’’European Foundation forNew Energy – EDF, Ecole Centrale Paris- Supelec, Paris, France, e-mail: [email protected] e-mail: [email protected]
Contributors xv