Tetsushi Yuge, Shinya Ozeki and Shigeru Yanagi
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…
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.
Details
Keywords
Tetsushi Yuge, Taijiro Yoneda, Nobuyuki Tamura and Shigeru Yanagi
This paper aims to present a method for calculating the top event probability of a fault tree with priority AND gates.
Abstract
Purpose
This paper aims to present a method for calculating the top event probability of a fault tree with priority AND gates.
Design/methodology/approach
The paper makes use of Merle's temporal operators for obtaining the minimal cut sequence set of a dynamic fault tree. Although Merle's expression is based on the occurrence time of an event sequence, the paper treats the expression as an event containing the order of events. This enables the authors to treat the minimal cut sequence set by using the static fault tree techniques. The proposed method is based on the sum of disjoint products. The method for a static FT is extended to a more applicable one that can deal with the order operators proposed by Merle et al.
Findings
First, an algorithm to obtain the minimal cut sequence set of dynamic fault trees is proposed. This algorithm enables the authors to analyze reasonably large scale dynamic fault trees. Second, the proposed method of obtaining the top event probability of a dynamic fault tree is efficient compared with an inclusion‐exclusion based method proposed by Merle et al. and a conventional Markov chain approach. Furthermore, the paper shows the top event probability is derived easily when all the basic events have exponential failure rates.
Originality/value
The methodology presented shows a new solution for calculating the top event probability of dynamic fault trees.