Fault-Tree Analysis by Fuzzy Probability

Tanaka, Hideo; Fan, L. T.; Lai, F. S.; Toguchi, K.

doi:10.1109/tr.1983.5221727

Cited by 354 publications

(211 citation statements)

References 5 publications

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“…Such data can be obtained from experts' evaluations or possibility of fuzzy clustering [26,27]. These possibilities correspond to a membership function of fuzzy data [28]. This demand for initial data representation is caused by the method of FDT induction.…”

Section: A the Repository For Data Collectionmentioning

confidence: 99%

“…Entropy and information have been introduced to the information theory as a probabilistic approach. The application of these measures assumes that the sum of possibilities of all values of every attribute equals 1 [26,27,28]. Note that the likelihood of attribute's value in terms of FDT induction is measured as confidence degree or degree of truth in this value.…”

Section: System Reliabilitymentioning

confidence: 99%

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Reliability Estimation of Healthcare Systems using Fuzzy Decision Trees

Levashenko

Zaitseva

Deserno

2016

Annals of Computer Science and Information Systems

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Abstract-Reliability is an important characteristic of any system. Healthcare systems are typical examples of such systems. In reliability engineering, such systems are considered as complex, inhomogeneous, and uncertain, and require special mathematical representations. The structure function is a suitable model representing real systems. Methods of system reliability evaluation based on the structure function are well established but deterministic. This restricts its use for uncertain or incomplete data. A structure function can be created only for system in which correlations of all components are indicated and all component states are known. In this paper, a new method for structure function construction is proposed. Incomplete data is analysed using Fuzzy Decision Trees (FDTs), where input and output attributes are interpreted as component states and values of the structure function, respectively. This method is applied to reliability analysis of healthcare system. For illustration, we considered the system laparoscopic surgery that has 4 components and 36 state vectors. In addition we evaluate proposed method by 3 benchmark's systems with 243, 108, and 512 state vectors, respectively. Two of these benchmarks have 5 components and one has 4 components. Uncertainty is simulated by randomly deleting between 5% and 90% of all state vectors before constructing the structure function. With 50% of deleted stages, the error rate is below 0.2% for all three systems. We conclude that FDT-based reliability analysis is applicable for incomplete data in medical systems, too.

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Section: A the Repository For Data Collectionmentioning

confidence: 99%

Section: System Reliabilitymentioning

confidence: 99%

Reliability Estimation of Healthcare Systems using Fuzzy Decision Trees

Levashenko

Zaitseva

Deserno

2016

Annals of Computer Science and Information Systems

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“…The first implementation of fuzzy method in the context of fault tree analysis was pioneered by Science Publications AJEAS (Tanaka et al, 1983), who treated imprecise probabilities of basic events as trapezoidal fuzzy numbers and employed the extension principle to describe the logical relationships leading to the top event. Furuta and Shiraishi (1984) also proposed a kind of importance measure but by means of max/min fuzzy operator and fuzzy integrals other than Tanaka's approach.…”

Section: Fault Tree Analysismentioning

confidence: 99%

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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Engineering design under uncertainty has gained considerable attention in recent years. A great multitude of new design optimization methodologies and reliability analysis approaches are put forth with the aim of accommodating various uncertainties. Uncertainties in practical engineering applications are commonly classified into two categories, i.e., aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arises because of unpredictable variation in the performance and processes of systems, it is irreducible even adding more data or knowledge. On the other hand, epistemic uncertainty stems from lack of knowledge of the system due to limited data, measurement limitations, or simplified approximations in modeling system behavior and it can be reduced by obtaining more data or knowledge. More specifically, aleatory uncertainty is naturally represented by a statistical distribution and its associated parameters can be characterized by sufficient data. If, however, the data is limited and can be quantified in a statistical sense, epistemic uncertainty can be considered as an alternative tool in such a situation. Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering design optimization. This study first attempts to provide a better understanding of uncertainty in engineering design by giving a comprehensive overview of its classifications, theories and design considerations. Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory. This overview includes the most recent results from theoretical research, computational developments and performance improvement of possibility theory and evidence theory with an emphasis on revealing the capability and characteristics of quantifying uncertainty from different perspectives. Possibility and evidence theory-based reliability methods have many advantages for practical engineering when compared with traditional probability-based reliability methods. They can work well under limited data while the latter need large amounts of information, more than possible in engineering practice due to aleatory and epistemic uncertainties. The possible directions for future work are summarized.

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“…These bounds are referred to as the zero-cut and one-cut, respectively, as they mark the sets where the membership function is greater than or equal to zero and one. (In general, an a-cut is the set where the membership function is greater than or equal to a [21].) The fuzzy failure rate or population may be listed as a four-element vector, with the one-cut surrounded by the zero-cut.…”

Section: Fuzzy Markov Modelsmentioning

confidence: 99%

“…We initially investigated methods similar to those used for fuzzy fault trees [10,11,21]. For these it can be suf®cient to propagate the various corresponding a -cut end points through the fault tree as if they were crisp, and then take the resulting extremal points as the corners of the output possibility distribution [10,13,14,21].…”

Section: Inappropriate Fuzzy Markov Modelsmentioning

confidence: 99%

Evaluating the reliability of prototype degradable systems

Leuschen

Walker

Cavallaro

2001

Reliability Engineering & System Safety

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The technique introduced in this paper is a new technique for analyzing fault tolerant designs under considerable uncertainty, such as seen in unique or few-of-a-kind devices in poorly known environments or pre-prototype design analyses. This technique is able to provide useful information while maintaining the uncertainty inherent in the original speci®cations. The technique introduced here is a logical extension of the underlying concepts of fuzzy sets and Markov models. Although originally developed for robotic systems, the technique is more broadly applicable. This paper develops fuzzy Markov modeling and uses it to analyze a speci®c robot designed for hazardous waste removal and speci®c types of electronic systems. q

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Fault-Tree Analysis by Fuzzy Probability

Cited by 354 publications

References 5 publications

Reliability Estimation of Healthcare Systems using Fuzzy Decision Trees

Reliability Estimation of Healthcare Systems using Fuzzy Decision Trees

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Evaluating the reliability of prototype degradable systems

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