• 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.

• Nuclear Engineering and Technology
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• 제44권4호
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• pp.405-414
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• 2012

In this paper, we propose a reliability estimation method for DI&C systems. At the system level, a fault tree model is suggested and Boolean algebra is used to obtain the minimal cut sets. At the component level, an exponential distribution is used to model hardware failures, and Bayesian estimation is suggested to estimate the failure rate. Additionally, a binomial distribution is used to model software failures, and a recently developed software reliability estimation method is suggested to estimate the software failure rate. The overall system reliability is then estimated based on minimal cut sets, hardware failure rates and software failure rates.

• Nuclear Engineering and Technology
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• 제50권6호
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• pp.854-859
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• 2018

Calculating minimal cut sets is a typical quantification method used to evaluate the top event probability for a fault tree. If minimal cut sets cannot be calculated or if the accuracy of the quantification result is in doubt, the Monte Carlo method can provide an alternative for fault tree quantification. The Monte Carlo method for fault tree quantification tends to take a long time because it repeats the calculation for a large number of samples. Herein, proposal is made to improve the quantification algorithm of a fault tree with circular logic. We developed a top-down iteration algorithm that combines the characteristics of the top-down approach and the iteration approach, thereby reducing the computation time of the Monte Carlo method.

• 한국통신학회논문지
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• 제13권5호
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• pp.379-389
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• 1988

본 논문에서는 통신방의 2-상태 스취칭 실패함수를 구하기 위한 알고리즘과 단섭간 신뢰도 계성방법을 제시하였다. 통신망을 그래프로 모형화하고, 이 그래프에 대한 일련의 행열변환을 함으로서 모든 통신통로를 차단하는 최초컷-\ulcornerV 행열을 구하였으며 최소 컷-\ulcornerV행열로부터 2-상태 스위칭 실패함수를 구하였다. 또한 2-상태 스위칭 실패함수에 확률변수를 대응시켜 통신망의 단점간 신뢰도를 계정하였다. 제안된 알고리즘을 설명하기 위하여 몇가지 예를 보였으며 복잡하고 규모가 큰 망에 대한 단점간 신뢰도를 계정하기 위해서 전산기 프로그램을 제시하였다.

• 한국경영과학회지
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• 제16권1호
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• pp.59-67
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• 1991

The hazard estimator is proposed for estimating system failure probability of a general network where all minimal cut sets are given. Theoretical variance of the hazard estimator is derived in a bridge system. It is demonstrated that variance of the hazard estimator is much smaller than that of the raw simulation estimator particularly for small arc failure probability.

• 대한안전경영과학회지
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• 제13권3호
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• pp.45-53
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• 2011

The research proposes seven elimination rules of redundant gates and blocks in Fault Tree Analysis (FTA) and Reliability Block Diagram (RBD). The computational complexity of cut sets and path sets is NP-hard. In order to reduce the complexity of Minimal Cut Set (MCS) and Minimal Path Set (MPS), the paper classifies generation algorithms. Moreover, the study develops six implementation steps which reflect structural importance (SI) and reliability importance (RI) from Reliability Centered Maintenance (RCM) that a priority of using the functional logic among components is to reduce (improve) the system unavailability (or availability). The proposed steps include efficient generation of state structure function by Rare Event Enumeration (REA). Effective use of importance measures, such as SI and ill measures, is presented based on the number and the size of MCS and MPS which is generated from the reference[5] of this paper. In addition, numerical examples are presented for practitioners to obtain the comprehensive understanding of six steps that is proposed in this research.

• Nuclear Engineering and Technology
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• 제55권6호
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• pp.2263-2275
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• 2023

In general, an internal fire events probabilistic safety assessment (PSA) model is quantified by modifying the pre-existing internal event PSA model. Because many pieces of equipment or cables can be damaged by a fire, a single fire event can lead to multiple internal events PSA initiating events (IEs). Consequently, when the fire events PSA model is quantified, inappropriate minimal cut sets (MCSs), such as duplicate MCSs, may be generated. This paper shows that single quantification of a hypothetical single-top fire event PSA model may generate the following four types of inappropriate MCSs: duplicate MCSs, MCSs subsumed by other MCSs, nonsense MCSs, and MCSs with over-counted fire frequencies. Among the inappropriate MCSs, the nonsense MCSs should be addressed first because they can interfere with the right interpretation of the other MCSs and prevent the resolution of the issues related to the other inappropriate MCSs. In addition, we propose a resolution process for each of the issues caused by these inappropriate MCSs and suggest an overall procedure for resolving them. The results of this study will contribute to the understanding and resolution of the inappropriate MCSs that may appear in the quantification of fire events PSA models.

• Nuclear Engineering and Technology
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• 제56권6호
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• pp.2092-2098
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• 2024

Probabilistic safety assessment (PSA) plays a critical role in ensuring the safe operation of nuclear power plants. In PSA, event trees are developed to identify accident sequences that could lead to core damage. These event trees are then transformed into a core-damage fault tree, wherein the accident sequences are represented by usual and complemented logic gates representing failed and successful operations of safety systems, respectively. The core damage frequency (CDF) is estimated by calculating the minimal cut sets (MCSs) of the core-damage fault tree. Delete-term approximation (DTA) is commonly employed to approximately solve MCSs representing accident sequence logics from noncoherent core-damage fault trees. However, DTA can lead to an overestimation of CDF, particularly when fault trees contain many nonrare events. To address this issue, the present study introduces a new zero-suppressed ternary decision diagram (ZTDD) algorithm that averts the CDF overestimation caused by DTA. This ZTDD algorithm can optionally calculate MCSs with DTA or prime implicants (PIs) without any approximation from the core-damage fault tree. By calculating PIs, accurate CDF can be calculated. The present study provides a comprehensive explanation of the ZTDD structure, formula of the ZTDD algorithm, ZTDD minimization, probability calculation from ZTDD, strength of the ZTDD algorithm, and ZTDD application results. Results reveal that the ZTDD algorithm is a powerful tool that can quickly and accurately calculate CDF and drastically improve the safety of nuclear power plants.

• 한국정보통신학회논문지
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• 제20권3호
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• pp.654-662
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• 2016

사고수목을 이루는 게이트나 기본사상이 많아질수록 정상사상 확률의 정확한 계산이 어려워진다. 이를 극복하기 위해 BDD 방법을 적용하면 중소형 사고수목의 경우 짧은 시간에 근사계산 없이 정확한 값을 구할 수 있다. CUDD 함수를 이용하여 사고수목을 BDD로 변환하고 그로부터 정상사상의 발생확률을 구하는 고장경로 탐색 알고리즘을 고안하였다. 후방탐색 알고리즘은 전방탐색 알고리즘보다 고장경로의 탐색과 확률계산 시간에서 효과적이다. 이 탐색 알고리즘은 BDD에서 고장경로를 찾는데 있어서 탐색시간을 줄일 수 있고, 해당 사고수목의 단절집합과 최소단절집합을 찾는 유용한 방법이다.

• 한국안전학회지
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• 제30권3호
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• pp.100-106
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• 2015

A module or independent subtree is a part of a fault tree whose child gates or basic events are not repeated in the remaining part of the fault tree. Modules are necessarily employed in order to reduce the computational costs of fault tree quantification. This quantification generates fault tree solutions such as minimal cut sets, minimal path sets, or binary decision diagrams (BDDs), and then, calculates top event probability and importance measures. This paper presents a new linear time algorithm to detect modules of large fault trees. It is shown through benchmark tests that the new method proposed in this study can very quickly detect the modules of a huge fault tree. It is recommended that this method be implemented into fault tree solvers for efficient probabilistic safety assessment (PSA) of nuclear power plants.