# Fault tree analysis considering sequence dependence and repairable input events

Tetsushi Yuge (Department of Electrical and Electronic Engineering, National Defense Academy, Yokosuka, Japan)
Shinya Ozeki (Department of Electrical and Electronic Engineering, National Defense Academy, Yokosuka, Japan)
Shigeru Yanagi (Department of Electrical and Electronic Engineering, National Defense Academy, Yokosuka, Japan)

ISSN: 1355-2511

Article publication date: 24 May 2013

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## Abstract

### Purpose

This paper aims to present two methods for calculating the steady state probability of a repairable fault tree with priority AND gates and repeated basic events when the minimal cut sets are given.

### Design/methodology/approach

The authors consider a situation that the occurrence of an operational demand and its disappearance occur alternately. We assume that both the occurrence and the restoration of the basic event are statistically independent and exponentially distributed. Here, restoration means the disappearance of the occurring event as a result of a restoration action. First, we obtain the steady state probability of an output event of a single‐priority AND gate by Markov analysis. Then, we propose two methods of obtaining the top event probability based on an Inclusion‐Exclusion method and by considering the sum of disjoint probabilities.

### Findings

The closed form expression of steady state probability of a priority AND gate is derived. The proposed methods for obtaining the top event probability are compared numerically with conventional Markov analysis and Monte Carlo simulation to verify the effectiveness. The result shows the effectiveness of the authors’ methods.

### Originality/value

The methodology presented shows a new solution for calculating the top event probability of repairable dynamic fault trees.

## Citation

Yuge, T., Ozeki, S. and Yanagi, S. (2013), "Fault tree analysis considering sequence dependence and repairable input events", Journal of Quality in Maintenance Engineering, Vol. 19 No. 2, pp. 199-214. https://doi.org/10.1108/13552511311315986

## Publisher

:

Emerald Group Publishing Limited

Copyright © 2013, Emerald Group Publishing Limited