Skip to main content

1995 | Buch

Reliability and Safety Analyses under Fuzziness

herausgegeben von: Professor Takehisa Onisawa, Professor Janusz Kacprzyk

Verlag: Physica-Verlag HD

Buchreihe : Studies in Fuzziness and Soft Computing

insite
SUCHEN

Über dieses Buch

This book provides a comprehensive, up-to-date account on recent applications of fuzzy sets and possibility theory in reliability and safety analysis. Various aspects of system's reliability, quality control, reliability and safety of man-machine systems fault analysis, risk assessment and analysis, structural, seismic, safety, etc. are discussed. The book provides new tools for handling non-probabilistic aspects of uncertainty in these problems. It is the first in this field in the world literature.

Inhaltsverzeichnis

Frontmatter

Introductory Sections

Frontmatter
Foundations of Reliability and Safety
Abstract
Basic notions and ideas used in reliability and safety analysis are presented. The outline of fundamental methods of analysis is given.
Janusz Karpiński, Włodzimierz Lewin, Jerzy Rudnicki
Brief Introduction to Fuzzy Sets
Abstract
We present a brief introduction to fuzzy sets theory for the interested readers who has not yet been exposed to this area. Particular emphasis is on basic elements and definitions, and to those which are relevant for the topics covered by this volume. First, the concept of a fuzzy set is presented as a formal means for dealing with the imprecision of meaning, caused mainly by the use of a natural language; such an imprecision is meant to be related to a gradual membership of elements. This is followed by main operations on fuzzy sets, the concepts of cardinality, a fuzzy relation, etc. Then, the concept of a fuzzy number is sketched. Basic operations on fuzzy numbers are dealt with with emphasis on the practically most relevant case of triangular and/or trapezoid fuzzy numbers.
Mario Fedrizzi, Janusz Kacprzyk

Reliability and Safety Analyses under Fuzziness: General Issues

Frontmatter
System Reliability from the Viewpoint of Evaluation and Fuzzy Sets Theory Approach
Abstract
Fuzziness and subjectivity are inherent in a system reliability analysis. This paper mentions the fuzziness and the subjectivity in estimation of a failure probability and an error probability, in modification of the failure probability and the error probability taking the influence of environmental conditions into consideration, in estimation of the dependence level, in evaluation of system reliability and safety. This paper also mentions one of fuzzy sets theory approaches in the system reliability analysis to deal with the fuzziness and the subjectivity. In this approach subjective unreliability measure represented by a fuzzy set is used, and informations on reliability, e.g., reliability estimate, dependence level estimate, are represented by natural language.
Takehisa Onisawa
Issues in Possibilistic Reliability Theory
Abstract
Recently, alternative models for the classical reliability theory based upon fuzzy set theory and related theories, are proposed to solve the problems of the classical approach. Our model is based upon a combination of multistate structure functions and possibility theory. In this paper, we present a congruence relation on the complete lattice of structure functions, that links several concepts of the theory of multistate structure functions and the possibilistic reliability theory. Some important possibilistic reliability bounds are established and, finally, we apply the theoretic concepts to some concrete examples.
Bart Cappelle, Etienne E. Kerre
Coherent Systems in Profust Reliability Theory
Abstract
Profust reliability theory is based on the probability assumption and the fuzzy-state assumption. In an attempt to provide a uniform foundation for profust reliability theory, in this paper we introduce the concept of coherent systems and distinguish two classes of systems: closely coherent systems and loosely coherent systems. To formulate the relationships between system reliabilities and component reliabilities, we present a number of general results, results concerning convexity, and results concerning unimodality. It is argued that for a coherent system, component reliability improvements don’t certainly enhance the system reliability.
Kai-Yuan Cai, Chuan-Yuan Wen, Ming-Lian Zhang
The Usefulness of Complete Lattices in Reliability Theory
Abstract
The main aim of this paper is to show how lattice theory in the very next future will be a useful tool in analysing complex real reliability problems, not properly modelled within classical reliability theory. The introduction of a complete lattice as a state space appears not only of theoretical importance that allows to understand several phenomena with respect to reliability theory better, but as a need claimed from practical engineering. Two important topics are discussed in this general framework: incomparability of component and system states and the duality principle. The strong relationship between the ideas of fuzzy set theory and the ideas that led to the introduction of the theory of multistate structure functions will become clear.
Javier Montero, Bart Cappelle, Etienne E. Kerre

Fault Tree Analysis Using Fuzzy Sets and Possibility Theory

Frontmatter
Multi State Fault Tree Analysis Using Fuzzy Probability Vectors and Resolution Identity
Abstract
In this paper, we propose a method of estimating top event fuzzy probability of a fault tree in case of a system consisting of multistate elements. To the best of our knowledge, no such attempt has ever been made in this direction in the past. Beta fuzzy probability vectors, as proposed by Stein [9], are used to model the joint-possibility distribution of multistate elements. The use of resolution identity keeps the computational requirement at its minimum. However, the estimation procedure is based on Zadeh’s extension principle.
Krishna B. Misra, K. P. Soman
Fuzzy Fault Tree Analysis : Case Studies
Abstract
Estimation of the fuzzy probability of occurrence of an hazardous event (such as: accidental release of chemicals) taking recourse to Fuzzy Sets Theory (FST) is the topic of immediate relevance in Probabilistics Risk Assessment for Chemical Industry. The paper relates to fuzzification of fault trees of 15000 MT capacity atmospheric storage tank and nitric acid reactor. The case studies on fuzzy fault tree analysis using available interfailure statistics of process control instruments brings out its utility over the conventional probabilistic approach.
A. W. Deshpande, P. Khanna
Faes — Fault Analysis Expert System
Abstract
In the development of expert systems, the process of acquiring knowledge from the domain expert and translating it to a form which the expert system can understand, is costly and time consuming. Also, expert systems available for fault isolation, detection and assessment are not fully matured. In this paper we will describe a system that is capable of automating the knowledge acquisition process, translating that knowledge into a fully validated knowledge base, and using this knowledge base for fault detection.
M. Schneider, A. Kandel

Life Time Analysis and Fuzzy Sets

Frontmatter
Reliability Estimation based on Fuzzy Life Time Data
Abstract
Real life time data are usually more or less fuzzy. Therefore it is necessary to generalize statistical estimation of the reliability characteristics. For life time data in form of fuzzy numbers x* with characterizing function ξ(.) this is possible and explained in the paper. Especially classical parameter estimations for stochastic life time models and the concept of the empirical reliability function as well as Bayesian reliability estimation procedures are generalized. Moreover the important technique of accelerated life testing is revisited in face of non-precise observed life times.
R. Viertl, W. Gurker
Lifetime Tests for Imprecise Data and Fuzzy Reliability Requirements
Abstract
The paper deals with the problem of the estimation of the average lifetime when observed survival are described by fuzzy numbers. The fuzzy estimator of the average lifetime is given. A simple method for the verification of reliability requirement is proposed.
Olgierd Hryniewicz

Reliability and Quality Control in Engineering Systems

Frontmatter
Reliability Behavior of Combined Hardware-Software Systems
Abstract
With the recognization that software reliability behavior is fuzzy or possibilistic, rather than probabilistic, in nature, and the assumption that hardware reliability behavior is probabilistic in nature, in this paper we show how to integrate fuzzy methodology and probabilistic methodology to characterize combined hardware-software reliability behavior. In concrete, the notions of canonical computer, possibilistic survival (PS-) function, and possibilistic vulnerary (PV-) function are introduced, and the combined hardware-software reliability behavior is demonstrated, respectively, for canonical computers, series computer systems and parallel computer systems. Thus this paper provides basic concepts and fundamental analysis and modeling methodology to characterize combined hardware-software reliability behavior of computer systems.
Kai-Yuan Cai, Chuan-Yuan Wen, Ming-Lian Zhang
An Application of Fuzzy Set Theory to Reliability Analysis
Reliability Prediction for Equipment Using Fuzzy Inference
Abstract
Fuzzy estimation is made of the reliability of an actual piece of electronic equipment, as measured by the mean time between failures (MTBF). This is then compared with actual MTBF field data.
Tadashi Murata
Application of Fuzzy Relational Modelling to Industrial Product Quality Control
Abstract
Industrial product quality control is a typical mathematical programming and optimization problem. Unfortunately, complete and precise models are not always available for many industrial processes. A fuzzy relation modelling approach is proposed to describe approximate relationships among system variables and reconcile empirical equations. Symmetric fuzzy decision-making is transformed into a non-linear function maximization problem. The approach is applied to optimization of a wood chip refining process. It is used either to improve pulp quality within the refiner operation range, or to reduce operation costs while maintaining an acceptable pulp quality.
Y. Qian, P. J. C. Tessier, G. A. Dumont
An Application of Fuzzy Structural Modeling to Relation Diagram Method in Quality Control
Abstract
Fuzzy sets theory is relatively little known to the sphere of quality control(QC)/quality management (QM). In the clerical, sales and research and development departments, however, objective numerical data are sometimes hard to gather, and the need to handle subjective data arises quite often.
The Relation Diagram Method, one of “the Seven Management Tools for QC”, is employed to solve a complex problem, such as out-of-contol caused by human factors in production process, by means of arrangement of cause and effect relationships of a problem. In applying the Relation Diagram Method to complex relationships among many elements of causes and/or results in the problem to be solved, it is often desirable and sometimes essential to create hierarchies. However, the process of rearranging elements in a hierarchy is not dealt with in the existing Relation Diagram Method.
In order to deal with such a relationship practically and systematically, the author proposes to create a hierarchy and rearrange the elements in a relation diagram by applying the Fuzzy Structural Modeling, which is developed on the basis of the fuzzy sets theory.
In order to demonstrate how the proposed method works, a practical example is given in which the structure of the relation diagram has been successfully identified and the usefulness of applying the Fuzzy Structural Modeling to relation diagrams is confirmed.
Shin’ya Nagasawa

Reliability of Man-Machine Systems

Frontmatter
Human Reliability Analysis with Fuzzy Integral
Abstract
A method of human reliability analysis (HRA) in the field of large scale plant operations is presented in this work. The fuzzy integral methodology was applied to provide a clear mathematical basis of the expert judgement required in human reliability analysis (HRA). Also, a method named the analytic hierarchy process (AHP) was introduced for supporting overall decision-making associated with the improvement of human reliability. The effectiveness of the proposed method is demonstrated through an application to decision-making on operability improvement of a process cooling system.
Takashi Washio, Masaharu Kitamura
Fuzzy Reliabilty Analysis of Labour (Man-Machine) Systems
Abstract
This article discloses an approach to model construction for assessment of reliability and quality of labour (man-machine) systems functioning using probabilistic-time figures.
The suggested approach is based upon composition of two types of models: (a) probabilistic-algorithmic models of labour process with parameters of labour operations in fuzzy number form; (b) logical- linguistic models of labour operations in fuzzy logical proposition.
A. Rotshtein

Safety and Risk Analyses

Frontmatter
Risk Index and Application of Fuzzy Logic
Abstract
A “risk index method” is proposed. This method provides the framework for different risk considerations and supports decision making under uncertainty. The simple concept is based on probabilistic risk analysis and uses some elements of fuzzy logic. Risk results are displayed on an index scale which is both qualitative and quantitative.
Christian Preyssl, Yasushi Nishiwaki
Risk-Based Ranking in Inspection of Industrial Facilities
Abstract
Inspection can play a significant role in reducing the likelihood of unexpected structural failures. However, for many critical components and systems that are required to maintain pressure boundary integrity or that are subjected to severe service conditions, inspection requirements for these vital components are either established based upon prior experience and engineering judgment or are nonexistent. Most inspection requirements or guidelines, if they exist, are usually established with only an implicit consideration of risk.
Recent catastrophic structural failures over the past decade highlight the societal need to relate more explicitly risk and uncertainty with inspection programs. In this study, risk-based methods with uncertainty evaluation and propagation were developed for the purpose of developing inspection strategies. Interval analysis was used for this purpose which is a form of fuzzy arithmetic. The methods result in establishing priority ranking lists for failure modes and components where actions need to be taken accordingly. The ranking priority lists for inspection purposes were based on the assessments of the probabilities of failure, resulting consequences, expected human and economic risks and the uncertainties associated with these assessments.
Ahmed A. Ibrahim, Bilal M. Ayyub
A Probabilistic-Fuzzy Model for Seismic Hazard
Abstract
A probabilistic-fuzzy model for seismic hazard analysis is developed. The proposed model is able to reproduce both the randomness and the imprecision in conjunction with earthquake occurrences. Results of this study are (a) membership functions of both peak ground accelerations associated with a given probability of exceedance and probabilities of exceedance associated with a given peak ground acceleration, and (b) characteristic values of membership functions at each location of interest. The proposed probabilistic-fuzzy model for assessment of seismic hazard is successfully applied to the Wasatch Front Range in Utah in order to obtain the seismic maps for different annual probabilities of exceedance, different peak ground accelerations, and different time periods.
Dan M. Frangopol, Kappyo Hong
Seismic Reliability Analysis of Existing Structures Based on Fuzzy Probability
Abstract
This paper provides a reliability analysis of existing bridge structures for earthquake loads. Using a fuzzy graph and fuzzy relation, an attempt is made to consider the effect of structural deterioration in the evaluation of structural reliability. The analysis method gives the final result in the form of fuzzy probability, which can provide more information to the reliability analysis of the structure in future. Several numerical examples are presented to demonstrate the applicability of the method proposed here.
Hitoshi Furuta, Masata Sugito, Shin-ya Yamamoto, Naruhito Shiraishi
Combined Probability-Possibility Evaluation Theory for Structural Reliability
Abstract
In structural identification and planning, as pointed by Yao and Natke (1991), it is very important to evaluate the uncertainties of future loads and structural responses. In this paper, probability functions in which additive law holds are combined with possibility functions in which maxitive law holds, so that their evaluation measures belong to a kind of fuzzy measures instead of probability measures. By using their joint evaluation distributions and measures, one can evaluate the uncertain strength of parallel or serial structural systems and the survival or fracture possibility of structures. This paper presents some examples of case studies and shows that the proposed combined probability-possibility evaluation theory is effective to evaluate the combined objective and subjective reliability of structures from practical and theoretical points of view.
Hiroshi Kawamura, Yasuhiko Kuwamoto
Reliability Assessment Using Variance Reduction Techniques Based on Fuzzy System Performance
Abstract
Classical reliability methods require a crisp definition of system failure according to some performance measure that is of interest to an analyst. Therefore, they do not consider any form of uncertainty in the system failure. This limitation might result in reliability assessments that are not realistic. The uncertainty associated with qualifying the performance of the system as inadequate, i.e., failed, should be considered in reliability assessment. The objective of this contribution is to generalize currently used reliability assessment methods by treating failure as a fuzzy event. Therefore, the reliability of the system can be provided over a nonperformance spectrum. Monte Carlo simulation with variance reduction techniques will be used in the computation of the reliability.
Kwan-Ling Lai, Bilal M. Ayyub
Metadaten
Titel
Reliability and Safety Analyses under Fuzziness
herausgegeben von
Professor Takehisa Onisawa
Professor Janusz Kacprzyk
Copyright-Jahr
1995
Verlag
Physica-Verlag HD
Electronic ISBN
978-3-7908-1898-7
Print ISBN
978-3-662-12913-5
DOI
https://doi.org/10.1007/978-3-7908-1898-7