Quantification of temporal fault trees based on fuzzy set theory

© Springer International Publishing Switzerland 2014. Fault tree analysis (FTA) has been modified in different ways to make it capable of performing quantitative and qualitative safety analysis with temporal gates, thereby overcoming its limitation in capturing sequential failure behaviour. However, for many systems, it is often very difficult to have exact failure rates of components due to increased complexity of systems, scarcity of necessary statistical data etc. To overcome this problem, this paper presents a methodology based on fuzzy set theory to quantify temporal fault trees. This makes the imprecision in available failure data more explicit and helps to obtain a range of most probable values for the top event probability

A Fuzzy Probability Algorithm for Evaluating the AP1000 Long Term Cooling System to Mitigate Large Break LOCA

Components of nuclear power plants do not always have historical failure data to probabilistically evaluate their reliability characteristics. To overcome this drawback, an alternative approach has been proposed by involving experts to qualitatively justifybasic event likelihood occurences. However, expert judgments always involve epistemic uncertainty and this uncertainty needs to be quantified. Existing fault tree analysis quantifies uncertainty using Monte Carlo simulation, which is based on probability distributions. Since expert judgments are not described in probability distributions, Monte Carlo simulation is not appropriate for evaluating epistemic uncertainty. Therefore, a new approach needs to be developed to overcome this limitation. This study proposes a fuzzy probability algorithmtoevaluate epistemic uncertainties in fault tree analysis.In the proposed algorithm, fuzzy probabilities are used to represent epistemic uncertainties of basic events, intermediate events, and the top event. To propagate and quantify epistemic uncertainty in fault tree analysis, a fuzzy multiplication rule and a fuzzy complementation rule are applied to substitute the AND Boolean and OR Boolean gates, respectively. To see the feasibility and applicability of the proposed algorithm, a case-based experiment on uncertainty evaluation of the AP1000 long term cooling system to mitigate the large break loss of coolant accident is discussed.The result shows that the best estimate probability to describe the failure of AP1000 long term cooling system generated by the proposed algorithmis3.15×10-11, which is very closed to the reference value of 1.11×10-11.This result confirms that the proposed algorithm offers a good alternative approach to quantify uncertainties in probabilistic safety assessment by fault tree analysis.Received:22 October 2014; Revised: 24 June 2015; Accepted: 29 June 201

A Fuzzy Probability Algorithm for Evaluating the AP1000 Long Term Cooling System to Mitigate Large Break LOCA

Components of nuclear power plants do not always have historical failure data to probabilistically evaluate their reliability characteristics. To overcome this drawback, an alternative approach has been proposed by involving experts to qualitatively justifybasic event likelihood occurences. However, expert judgments always involve epistemic uncertainty and this uncertainty needs to be quantified. Existing fault tree analysis quantifies uncertainty using Monte Carlo simulation, which is based on probability distributions. Since expert judgments are not described in probability distributions, Monte Carlo simulation is not appropriate for evaluating epistemic uncertainty. Therefore, a new approach needs to be developed to overcome this limitation. This study proposes a fuzzy probability algorithmtoevaluate epistemic uncertainties in fault tree analysis.In the proposed algorithm, fuzzy probabilities are used to represent epistemic uncertainties of basic events, intermediate events, and the top event. To propagate and quantify epistemic uncertainty in fault tree analysis, a fuzzy multiplication rule and a fuzzy complementation rule are applied to substitute the AND Boolean and OR Boolean gates, respectively. To see the feasibility and applicability of the proposed algorithm, a case-based experiment on uncertainty evaluation of the AP1000 long term cooling system to mitigate the large break loss of coolant accident is discussed.The result shows that the best estimate probability to describe the failure of AP1000 long term cooling system generated by the proposed algorithmis3.15×10-11, which is very closed to the reference value of 1.11×10-11.This result confirms that the proposed algorithm offers a good alternative approach to quantify uncertainties in probabilistic safety assessment by fault tree analysis.Received:22 October 2014; Revised: 24 June 2015; Accepted: 29 June 201

Conditional probability of actually detecting a financial fraud - a neutrosophic extension to Benford's law

This study actually draws from and builds on an earlier paper (Kumar and Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to the problem of determining the conditional probability that a financial fraud has been actually committed, given that no Type I error occurred while rejecting the null hypothesis H0: The observed first-digit frequencies approximate a Benford distribution; and accepting the alternative hypothesis H1: The observed first-digit frequencies do not approximate a Benford distribution. We have also suggested a conceptual model to implement such a neutrosophic fraud detection system.Comment: 9 page

Cohesion and Complex System Structure

In the self-organizing complex dynamical systems that form holarchies, the decisions (or reactions) of their components (constituents) sometimes are crucial because they may involve the proper existence of the system. Additionally, in the real world, these components are immersed in highly complex environments of which have an incomplete or inadequate knowledge and they can’t be completely consistent about their preferences and their beliefs, can show a bounded rationality, etc. All these circumstances affect the way in which the components not only behave, but also emerge and disappear. In this work the necessary and sufficient conditions previously given for the holons formation are reviewed in the light of these facts using for the uncertainty/randomness handling the fuzzy probabilities theory (thus modeling the decision making process through the fuzzy decision making under risk theory), and, from these conditions, the concept of holon cohesion is derived and introduced as a generalization of the reliability of a system

Portfolio Optimization Efficiency Test Considering Data Snooping Bias

Background: In the portfolio optimization area, most of the research is focused on in-sample portfolio optimization. One may ask a rational question of what the efficiency of the portfolio optimization strategy is and how to measure it. Objectives: The objective of the paper is to propose the approach to measuring the efficiency of the portfolio strategy based on the hypothesis inference methodology and considering a possible data snooping bias. The proposed approach is demonstrated on the Markowitz minimum variance model and the fuzzy probabilities minimum variance model. Methods/Approach: The proposed approach is based on a statistical test. The null hypothesis is that the analysed portfolio optimization strategy creates a portfolio randomly, while the alternative hypothesis is that an optimized portfolio is created in such a way that the risk of the portfolio is lowered. Results: It is found out that the analysed strategies indeed lower the risk of the portfolio during the market’s decline in the global financial crisis and in 94% of the time in the 2009-2019 period. Conclusions: The analysed strategies lower the risk of the portfolio in the out-of-sample period

Reliability Analysis of Metro Door System Based on Fuzzy Multi-State Bayesian Network

Considering the shortcomings of the fault tree analysis (FTA) method in the reliability analysis of metro door systems, Bayesian network (BN) and fuzzy theory were introduced to establish the failure probability model of a metro door system. A fault tree of the metro door system was established based on the structure of the metro door, the operation data record and the practical experience of relevant engineers. The BN of the metro door system was constructed based on the fault tree. For the problem that the prior probabilities of root nodes with missing data were unavailable, fuzzy theory was introduced to convert the expert language values on these missing data nodes to corresponding prior probabilities, which were substituted into the BN along with the root nodes whose prior probabilities were obtained from the operation fault data to calculate the leaf node probability. Cause analysis of the metro door system was performed with bi-directional reasoning of BN, which provided a way to find the key factors that caused door faults and the metro door system fault probabilities