LOGO Combining Fault Trees and Event Trees Seung Ki, Shin

2 Contents 1.Introduction 2.Event Tree (ET) & Fault Tree (FT) 3.Combining ET & FT 3.1. Combine ET & SFT 3.2. Combine ET & DFT 4.Summary & Further Study

3 Introduction ▪ For reliability analysis of a certain system, it is required to develop analysis maps about failures of the system. ▪ There are two ways to develop this ; fault tree analysis (FTA) and event tree analysis (ETA). ▪ When analyzing the reliability of a complex system, combining these two ways is needful.

4 Event Tree Analysis ▪ Event Tree is a graphical representation of mitigating or aggravating events that may occur in response to some initiating event in the system. ▪ Inductive and forward logic representation. ▪ This is helpful to identify the consequences that can result in the following occurrence of a potentially hazardous event.

5 Fault Tree Analysis ▪ Fault tree (FT) is constructed by defining the TOP undesired event and then using backward logic to define causes. ▪ Basic events at the bottom of the fault tree are linked via logic symbols (known as gates) to one or more higher-level events. ▪ Deductive and backward logic representation.

6 Fault Tree Analysis ▪ This is useful to analyze the failure of each part in the whole system. ▪ There are two kinds of fault trees ▫ Static Fault Tree → composed of Boolean gates ▫ Dynamic Fault Tree → adding sequential notion to SFT (PAND, SPARE, SEQ, FDEP gate)

7 Combining ET & FT ◈ Relation Between ET & FT ▪ Although there exist differences between ET and FT, they are closely related to each other. ▪ Branch point events of ET can be defined using FT structure. ▪ So, the probability of the top event of the FT serves as the branch probability for the ET.

8 Combining ET & FT ◈ Combining ET & SFT

9 Combining ET & FT ◈ Combining ET & SFT ▪ Quantification can be achieved by multiplying the frequency of the initiator and the probabilities of passing along each branch leading to an outcome scenario. ▪ The probability of each branch point can be obtained by Inclusion-Exclusion Expansion (IEE) or Minimal Cut Upper Bound (MCUB) method. ▫ IEE → ▫ MCUB → )

10 Combining ET & FT ◈ Combining ET & DFT ▪ Static fault trees are limited to modeling system failures without sequential relationships among component failures. ▪ It is required to combine event tree and dynamic tree. ▪ This methodology will be illustrated by a hypothetical bank- account-access example.

11 Combining ET & DFT ◈ Bank-account-access example ▪ X1 → the failure of the first way to access a bank account, which is achieved by a customer operating his/her own personal computer through Internet ▪ X2 → the failure of the second way, through a teller operating one of all three terminals in the bank ▪ X3 → the failure of the third way, done by the bank computer system manager operating on a server directly SymbolDefinition PPersonal computer of the customer TTerminal in the bank A/BPrimary / backup server in the bank DLocal power supply service EBackup power supply service in the bank FUPS for the customer’s computer

12 Combining ET & DFT ◈ Fault trees of each subsystem

13 Combining ET & DFT ◈ Markov chain for the dynamic module

14 Combining ET & DFT ◈ Event trees ▪ Dynamic module ▪ Static module

15 Combining ET & DFT Possible / impossible result OXOXOXOO

16 Summary & Further Study ▪ Combining event trees and fault trees is very profitable to analyze the reliability and safety of a system. ▪ To analyze the actual system well, the introduction of fault trees is necessary. ▪ One way of combining event trees and dynamic trees was presented based on a hypothetical example. ▪ Considering the diversity of dynamic systems, this method has just started at the beginning, so we need consider enough different examples, which would be helpful to find their common features.

17 References ▪ 박창규, 하재주, “ 확률론적 안정성 평가 ”, ▪ H. Xu, JB. Dugan, “Combining Dynamic Fault Trees and Event Trees for Probabilistic Risk Assessment”, IEEE, ▪ R. Manian, DW. Coppit, KJ. Sullivan, JB. Dugan, “ Bridging the Gap Between Systems and Dynamic Fault Tree Models”, IEEE, ▪ W. Keller, M. Modarres, “A historical overview of probabilistic risk assessment development and its use in the nuclear power industry”, Reliability Engineering and System Safety, ▪