Reliability and Safety Analyses under Fuzziness

Reliability and Safety Analyses under Fuzziness

Studies in Fuzziness Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Siences ul. Newelska 6 01-447 Warsaw, POLAND E-mail: kacprzyk@ibspan.waw.pl Vol. I. J. Kacprzyk and M. Fedrizzi (Ed. ) Fuzzy Regression Analysis. 1992 ISBN 3-7908-059\-2 (ISBN 83-85262-07-5) Vol. 2 A. M. Delgado et al. (Ed. ) Fuzzy Optimization, 1994 ISBN 3-7908-0749-4 Vol. 3. A. Geyer-Schulz Fuzzy Rule-Based Expert Systems and Genetic Machine Learning, 1995 ISBN 3-7908-0830-X

Takehisa Onisawa. Janusz Kacprzyk Editors Reliability and Safety Analyses under Fuzziness With 106 Figures Springer-Verlag Berlin Heidelberg GmbH

Professor Takehisa Onisawa Institute of Engineering Mechanics University oftsukuba 1-1-1, Tennodai Tsukuba 305, Japan Professor Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw, Poland ISBN 978-3-662-12913-5 CIP-Titelaufnahme der Deutschen 8ibliothek Reliability and safety analyses under fuzziness I Takehisa Onisawa; Janusz Kacprzyk, ed. (Studies in fuzziness; VoI. 4) ISBN 978-3-662-12913-5 ISBN 978-3-7908-1898-7 (ebook) DOI 10.1007/978-3-7908-1898-7 NE: Onisawa, Takehisa lhrsg.); GT This work is subject to copyright. AII rights are reserved, whether the whole or part ofthe material is concemed, specifically tbe rights of translation, reprinting, reuse of illustration, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication oftbis publication or parts tbereofis ooly permitted under the provisions ofthe German Copyright Law ofseptember 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. Violations fali under the prosecution act ofthe German Copyright Law. Springer-Verlag Berlin Heidelberg 1995 Originally published by Physica-Verlag Heidelberg in 1995 The use of registered names, trademarks, etc. in tbis publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 8812202-543210 - Printed on acid-free paper

FOREWORD In recent years fuzzy sets theory has been playing a remarkable role in many diverse areas of science and technology, notably in control and knowledge-based systems. Reliability and safety analyses of systems is also one of the most important fields in which fuzzy sets theory may find applications. The collection of contributions to this volume represents numerous important developments in reliability and safety analyses under fuzziness. It is very exciting to learn what has been successfully achieved in this area by applying fuzzy theory. Fuzzy theory has certainly brought about a new scope in the world of probabilities. Obviously probability theory has been and still is considered to be a dominant tool to deal with reliability and safety issues. Hence fuzzy theory researchers are faced with a lot of criticism from the probabilists in this area. However, as a matter of fact, fuzzy theory, for example possibility theory, is compatible with probability theory. What we have shown so far is that probability theory needs not be replaced by fuzzy theory, but rather that the former works much better in applications if it is combined with the latter. In fact, it is said that there are two essential uncertainties in the field of reliability and safety analyses: one is a probabilistic uncertainty which is more relevant for mechanical systems and the natural environment, and the other is fuzziness (imprecision) caused by the existence of human beings in systems. The classical probability theory alone is therefore not sufficient to deal with uncertainties in humanistic system. In such a context this collection of works will put a milestone in the arguments of probability theory and fuzzy theory. This volume covers fault analysis, life time analysis, reliability, quality control, safety analysis and risk analysis. The works of such a wide range were collected by two editors, Professor Takehisa Onisawa and Professor Janusz Kacprzyk. The editors have played a major role in the development of these important branches of fuzzy theory. Thus I have no doubt of the success of this volume. Tokyo, June, 1994 Michio Sugeno

Table of Contents Foreword M. Sugeno v 1. INTRODUCTORY SECTIONS Foundations of reliability and safety J. Karpiflski, W. Lewin and J. Rudnicki Brief introduction to fuzzy ~ts M. Fedrizzi and 1. Kacprzyk 3 31 2. RELIABILITY AND SAFETY ANALYSES UNDER FUZZINESS: GENERAL ISSUES System reliability from the viewpoint of evaluation and fuzzy sets theory approach T.Onisawa Issues in possibilistic reliability theory B. Cappelle and E.B. Kerre Coherent systems in profust reliability theory K-Y. Cai, Ch.-Y. Wen and M.-L. Zhang The usefulness of complete lattices in reliability theory J. Montero, B. Cappelle and B.B. Kerre 43 61 81 95 3. FAULT TREE ANALYSIS USING FUZZY SETS AND POSSmILITY THEORY Multi state fault tree analysis usingfuzzy probability vectors and resolution identity 113 KB. Misra and KP. Soman Fuzzy fault tree analysis: case studies 126 A.W. Deshpande and P. Khanna

VIII FAES - Fault analysis expert system M. Schneider and A. Kandel 142 4. LIFE TIME ANALYSIS AND FUZZY SETS Reliability estimation based onfuzzy life time data 153 R. Viertl and W. Gurker Lifetime tests for imprecise data and fuzzy reliability requirements 169 O. Hryniewicz 5. RELIABILITY AND QUALITY CONTROL IN ENGINEERING SYSTEMS Reliability behaviorof combined hardware-software systems 183 K.-Y. Cai, Ch.-Y. Wen and M.-L. Zhang An application of fuzzy set theory to reliability analysis: Reliability prediction for equipment usingfuzzy inference 196 T. Murata Application of fuzzy relational modelling to industrial product quality control 203 Y. Qian, PJ.C. Tessier and G.A. Dumont An application of fuzzy structural modeling to relation diagram method in quality control 217 S. Nagasawa 6. RELIABILITY OF MAN-MAClllNE SYSTEMS Human reliability analysis with fuzzy integral T. Washio and M. Kitamura Fuzzy reliability analysis of labour (man-machine) systems A. Rotshtein 233 245 7. SAFETY AND RISK ANALYSES Risk index and application of fuzzy logic Ch. Preyssl and Y. Nishiwaki Risk-based ranking in inspection of industrial facilities A.A. Ibrahim and B.M. Ayyub 273 285

IX A probabi/istic-juzzy model for seismic hazard 302 n.m. Frangopol and K. Hong Seismic reliability analysis of existing structures based on fuzzy probability 326 H. Furuta, M. Sugito, S. Yamamoto and N. Shiraishi Combined probability-possibility evaluation theory for structural reliability 341 H. Kawamura and Y. Kuwamoto Reliability assessment using variance reduction techniques based on fuzzy system performance 358 K.-L. Lai and B.M. Ayyub