• Journal of the Korean Statistical Society
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• 제29권3호
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• pp.297-306
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• 2000

An efficient method of constructing $textsc{k}$-minimal path sets to evaluate the reliability of a flow network is presented. The network is considered to be in a functioning state if it can transmit a maximum flow which is greater than or equal to a specified amount of flow, $textsc{k}$say, and a $textsc{k}$-minimal path set is a minimal set of branches that satisfies the given flow constraint. In this paper, under the assumption that minimal path sets of the network are known, we generate composite paths by adding only a minimal set of branches at each iteration to get $textsc{k}$-minimal path sets after possibly the fewest composition, and compute maximum flow of composite paths using only minimal path sets. Thereby we greatly reduce the possible occurrence of redundant composite paths throughout the process and efficiently compute the maximum flow of composite paths generated. Numerical examples illustrate the method.

• Nuclear Engineering and Technology
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• 제56권5호
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• pp.1603-1618
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• 2024

Emergency operation plans are indispensable elements for effective process safety management especially when unanticipated events occur under extreme situations. In the paper, a synthesis framework is proposed for the integration success path planning and performance analysis. Within the synthesis framework, success path planning is implemented through flow-directed signal tracing, renaming and reconstruction from a complete collection of Minimal Path Sets (MPSs) that are obtained using graph traversal search on GO-FLOW model diagram. The performance of success paths is then evaluated and prioritized according to the task complexity and probability calculation of MPSs for optimum action plans identification. Finally, an Auxiliary Feed Water System of Pressurized Water Reactor (PWR-AFWS) is taken as an example system to demonstrate the flow-directed MPSs search method for success path planning and performance analysis. It is concluded that the synthesis framework is capable of providing procedural guidance for emergency response and safety management with optimal success path planning under extreme situations.

• 품질경영학회지
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• 제28권1호
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• pp.105-118
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• 2000

In this paper, we consider an interconnection network, DRDT (Dual Receive Dual Transmit), that is a double-loop ring topology and adopts the concept of multiple packets transmission. For three types of DRDT configurations, we investigate some properties related to path sets and discuss the method for finding minimal path sets. Using the concept of the terminal reliability and the path sets approach, we evaluate the reliability of the DRDT networks and compare them with a single ring network and a unidirectional double-loop ring network.

• 한국안전학회지
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• 제3권2호
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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.

• 산업경영시스템학회지
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• 제12권20호
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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.

• 산업경영시스템학회지
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• 제24권63호
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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.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.689-701
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• 2021

The purpose of this paper is to optimize the number of source places required for the unique representation of the destination using the tools of graph theory. A subset S of vertices of a graph G is called a rational resolving set of G if for each pair u, v ∈ V - S, there is a vertex s ∈ S such that d(u/s) ≠ d(v/s), where d(x/s) denotes the mean of the distances from the vertex s to all those y ∈ N[x]. A rational resolving set is called minimal rational resolving set if no proper subset of it is a rational resolving set. In this paper we study varieties of minimal rational resolving sets defined on the basis of its complements and compute the minimum and maximum cardinality of such sets, respectively called as lower and upper rational metric dimensions for power of a path P_n analysing various possibilities.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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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.

• 대한전자공학회논문지
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• 제14권6호
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• pp.10-15
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• 1977

This paper proposes a simple and systematic method for the generation of the fault detection test sets for the combinational logic networks. Based on tile path sensitizing concept, the test patterns for the primary input gates of the network are defined, and then it is shown that, arranging these predefined test patterns according to the path sensitizing characteristics of the given network sturctures, the minimal complete test sets for the fan-out free combinational networks can be found easily. It is also shown that, taking into account the fan-out paths sensitizing compatibility, the proposed method can be extended to the irredundant reconvergent fan-out networks.

• 대한안전경영과학회지
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• 제14권1호
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• pp.225-233
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• 2012

The research discusses interrelationship of structural and reliability importance measures which used in the probabilistic safety assessment. The most frequently used component importance measures, such as Birnbaum's Importance (BI), Risk Reduction (RR), Risk Reduction Worth (RRW), RA (Risk Achievement), Risk Achievement Worth (RAW), Fussel Vesely (FV) and Critically Importance (CI) can be derived from two structure importance measures that are developed based on the size and the number of Minimal Path Set (MPS) and Minimal Cut Set (MCS). In order to show an effectiveness of importance measures which is developed in this paper, the three representative functional structures, such as series-parallel, k out of n and bridge are used to compare with Birnbaum's Importance measure. In addition, the study presents the implementation examples of Total Productive Maintenance (TPM) metrics and alternating renewal process models with exponential distribution to calculate the availability and unavailability of component facility for improving system performances. System state structure functions in terms of component states can be converted into the system availability (unavailability) functions by substituting the component reliabilities (unavailabilities) for the component states. The applicable examples are presented in order to help the understanding of practitioners.