Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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A Method of BDD Restructuring for Efficient MCS Extraction in BDD Converted from Fault Tree and A New Approximate Probability Formula

고장수목으로부터 변환된 BDD에서 효율적인 MCS 추출을 위한 BDD 재구성 방법과 새로운 근사확률 공식

  • Received : 2019.05.13
  • Accepted : 2019.06.04
  • Published : 2019.06.30
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Abstract

BDD is a well-known alternative to the conventional Boolean logic method in fault tree analysis. As the size of fault tree increases, the calculation time and computer resources for BDD dramatically increase. A new failure path search and path restructure method is proposed for efficient calculation of CS and MCS from BDD. Failure path grouping and bottom-up path search is proved to be efficient in failure path search in BDD and path restructure is also proved to be used in order to reduce the number of CS comparisons for MCS extraction. With these newly proposed methods, the top event probability can be calculated using the probability by ASDMP(Approximate Sum of Disjoint MCS Products), which is shown to be equivalent to the result by the conventional MCUB(Minimal Cut Upper Bound) probability.

이진결정도는 고장수목 해석에서 기존의 Boolean Logic 해석법의 잘 알려진 대체 방법이다. 고장수목의 규모가 커짐에 따라 계산에 필요한 컴퓨터 연산시간과 자원이 급격하게 증가한다. 이진결정도로부터 단절집합 및 최소단절 집합을 효과적으로 계산하기 위해 새로운 고장경로 탐색법과 고장경로 재구성 방법이 제안되었다. 고장경로 그룹화와 Bottom-Up 탐색법은 고장경로의 탐색에 효율적임을 증명하였고, 최소단절집합 계산을 위한 단절집합의 비교계산 횟수를 줄이기 위해 경로 재구성 방법을 사용할 수 있음을 증명하였다. 새로 제안된 방법을 적용하고, 기존의 근사확률 공식인 MCUB 확률공식과 동일한 새로운 ASDMP 확률공식을 사용하여 정상사상 확률을 계산 할 수 있다.

Keywords

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Fig. 1 Sample Fault Tree

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Fig. 2 BDD of Sample FT

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Fig. 3 FT for BDD Restructure

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Fig. 4 BDD 1

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Fig. 6 BDD 3

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Fig. 5 BDD 2

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Fig. 7 BDD 4

Table. 1 Bottom-Up Failure Path Search Algorithm

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Table. 2 Comparison of CS between Original BDD and Restructured BDD

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Table. 3 The Number of CS Comparisons for MCS Extraction

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Table. 4 Comparison of Exact & Approximate TEP

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