• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.79-84
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• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological spaces.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.3
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• pp.51-57
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• 1993

This paper develops 0($n^3$) algorithm to construct a cut-tree generated by Gomory-Hu algorithm. The algorithm only requires node sets defined by the minimal cut in each of the (n-1) maximal flow determinations. Merging computerized facility layout procedure that uses cut-tree concept to generate design skeletons with our algorithm requires less storage space than merging it with Gomory-Hu algorithm. Also, the cut-tree can easily be modified when the (n-1) minimal cut-sets are updated due to changes on arc capacities.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.12 no.20
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• pp.1-24
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• 1989

This paper takes aim at the reliability evaluation by application of Fault Tree Analysis and its computerization. FTA is one of the methods for evaluation of system reliability and safety analysis. The important characteristic of this paper is that computer program is written in the package program(dBaseIII+) by 16Bit/AT personal computer. The program consists of three program segments. (1) The minimal cut sets of the system fault tree are obtained by means of "Fault tree reduction algorithm" (2) The minimal path sets are obtained by inversion of the minimal cut sets determined from fault tree (3) The importance of the basic events which are presented in the minimal cut sets is obtained by means of structural importance analysis. In this paper, a Fault Tree Analysis is applied to a BAG FILTER which is a kind of dust collector.collector.

• Nuclear Engineering and Technology
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• v.24 no.1
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• pp.14-29
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• 1992

COMCAF, a computer code for the common-cause failure analysis, is developed to treat the common-cause failures in nuclear power plants. In the treatment of common-cause failures, the minimal cut sets of the system are obtained first without changing the fault-tree structure. The occurrence probabilities of the minimal cut sets are then calculated accounting for the common-cause failures among components in the same minimal cut set or in different minimal cut sets. The basic parameter model is used to model the common-cause failures between similar or identical components. For dissimilar components, the assumption of symmetry used in the basic parameter model is applied to the basic events affecting two or more components. The top event probability is evaluated using the inclusion-exclusion method. In addition to the common-cause failures of components in the same minimal cut sets, failures of components in the different minimal cut sets are also easily accounted for by this method. This study applied this common-cause failure analysis to the PWR auxiliary feedwater system. The results in the top event probability for the system are compared with those of no common-cause failures.

• Journal of the military operations research society of Korea
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• v.6 no.1
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• pp.119-124
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• 1980

An efficient algorithm which can be employed in obtaining the minimal cut sets of a fault tree containing repeated events is introduced. A sample fault tree illustrates this algorithm. Efficiency of an algorithm is defined as the ratio of the number of minimal cut sets to the number of cut sets determined by the algorithm. An efficiency of the proposed algorithm is compared with those of two existing algorithms : Fussell and Vesely's algorithm and Bengiamin et al. 's algorithm. The proposed algorithm is shown to be more efficient than the existing two algorithms.

• Journal of the Korean Society of Safety
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• v.3 no.2
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• pp.5-16
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• 1988

This study is conducted to evaluate the explosion of tolune storage tank in the petrochemical plant by Fault Tree Analysis. The conclusions are as follows; 1) Fault Tree diagram and the required computer program for evaluation of explosion accident is developed. 2) The probability of the top event, explosion accident, is $1.5\;{\times}\;10^{-8}$ per year, so there is almost no possibility of explosion during the life cycle of tank. However, the probability of Gate 6 and Gate 7 is 8.8 per month, therefore, attention should be paid to them for accident prevention. 3) The number of minimal cut sets is 67 sets which are not calculated the probability of each set, because of the lack of computer capacity. All the minimal cut sets should be examined case by case. However, it is necessary to be paid attention to COM1, 126, 131, and COM4 in minimal cut sets, because the number of appearance is so high. 4) The number path sets is 70 sets which are not calculated the probability of each set, because of the lack of computer capacity. It is very useful to prepare safety checklist by using this minimal path sets. Also, the events which appear many times, 123, COM5, 139, 127 and 128, are very high in reliability.

• Journal of the Korean Society of Safety
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• v.32 no.1
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• pp.41-46
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• 2017

In this paper, from making an electrical fire which is thought to be the most damaging among potential dangers as a top event, minimal cut sets (MCS) about it were analyzed. For this, components of a power substation were classified into 15 items. Failure rates and modes were extracted based on Korea Electrical Safety Corporation, IEEE Gold Book, and RAC. To analyze the top event (an electrical fire), main events were assorted into "safety devices for overcurrent" and "ampere meter of detecter". Failure of components was divided into failure of VCB, COS, and MCCB. A fault tree was composed of 3 AND gate, 5 OR gates and 17 basic events. Overlapped events among the basic events are things which occur from relevant components. They were attached to the tree by distinguishing identifiers. In case of FT, two minimal cut sets of "IO_METER", "MF_METER", "DO_MCCB" and "IO_METER", "MF_METER", "DO_VCB" take 46% of electrical fires. Therefore, about basic events which are included in the top two minimum cut sets, strict control is necessary.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.24 no.63
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• pp.33-43
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• 2001

To estimate the reliability of a large and complex network with a small variance, we propose two dynamic Monte Carlo sampling methods: the sequential minimal cut set (SMCS) and the sequential minimal path set (SMPS) methods. These methods do not require all minimal cut sets or path sets to be given in advance and do not simulate all arcs at each trial, which can decrease the valiance of network reliability. Based on the proposed methods, we develop the importance sampling estimators, the total hazard (or safety) estimator and the hazard (or safety) importance sampling estimator, and compare the performance of these simulation estimators. It is found that these estimators can significantly reduce the variance of the raw simulation estimator and the usual importance sampling estimator. Especially, the SMCS algorithm is very effective in case that the failure probabilities of arcs are low. On the contrary, the SMPS algorithm is effective in case that the success Probabilities of arcs are low.

• Fire Science and Engineering
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• v.31 no.6
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• pp.67-73
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• 2017

An aircraft maintenance hangar is a building that stores, maintains, and inspects expensive aircraft. The frequency of fire occurrence is low, but the resulting human and material damage can be very serious. Therefore, in this study, we conducted a qualitative analysis of the fire safety of the currently operating fire suppression systems for aircraft maintenance hangars using the Fault Tree method, and then performed a quantitative analysis using the failure rate data for the derived basic events and analyzed the importance of the minimal cut sets. As a result of the qualitative analysis by the minimal cut set, it was found that there were 14 accident paths that could be expanded to a large fire, due to the fire control failure of the aircraft hangar fire suppression system. The quantitative analysis revealed that, the probability of the fire expanding into a large one is $2.08{\times}E-05/day$. The analysis of the importance of the minimal cut set shows that four minimal cut sets, namely the fire detector and foam head action according to the zone and blocking of the foam by the aircraft wing and the fire plume, had the same likelihood of causing the fire to develop into a large one, viz. 24.95% each, which together forms the majority of the likelihood. It was confirmed for the first time by fault tree method that the fire suppression system of aircraft maintenance hangars is not suitable for fires under the aircraft wings and needs to be improved.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.121-135
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• 1999

This paper studies the problem of inverting minimal path sets to obtain minimal cut sets for complex system. We describe efficiency of inversion algorithm by the use of boolean algebra and we develop inclusion-exclusion algorithm and pivotal decomposition algorithm for reliability calculation of complex system. Several examples are illustrated and the computation speeds between the two algorithms are undertaken.