Fault Tree Interval Analysis of Complex Systems Based on Universal Grey Operation

Feng Zhang,Yameng Wang,Yang Gao,Shiwang Tan,Leilei Zhang

doi:10.1155/2019/1046054

Feng Zhang, Yameng Wang + Show 3 more

Open Access

https://doi.org/10.1155/2019/1046054

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Abstract

The objective of this study is to propose a new operation method based on the universal grey number to overcome the shortcomings of typical interval operation in solving system fault trees. First, the failure probability ranges of the bottom events are described according to the conversion rules between the interval number and universal grey number. A more accurate system reliability calculation is then obtained based on the logical relationship between the AND gates and OR gates of a fault tree and universal grey number arithmetic. Then, considering an aircraft landing gear retraction system as an example, the failure probability range of the top event is obtained through universal grey operation. Next, the reliability of the aircraft landing gear retraction system is evaluated despite insufficient statistical information describing failures. The example demonstrates that the proposed method provides many advantages in resolving the system reliability problem despite poor information, yielding benefits for the function of the interval operation, and overcoming the drawback of solution interval enlargement under different orders of interval operation.

Highlights

The fault tree analysis (FTA) method is typically applied as the main method in the reliability analysis of large systems [1,2,3]
The objective of this study is to propose a new operation method based on the universal grey number to overcome the shortcomings of typical interval operation in solving system fault trees
The traditional fault tree analysis method is based on a probability model; when there is a large set of failure samples and other sufficient statistical information describing the evaluated parts of a system, the uncertainty of bottom events can be quantified independently [5, 12]

Summary

Introduction

The fault tree analysis (FTA) method is typically applied as the main method in the reliability analysis of large systems [1,2,3]. The traditional fault tree analysis method is based on a probability model; when there is a large set of failure samples and other sufficient statistical information describing the evaluated parts of a system, the uncertainty of bottom events can be quantified independently [5, 12]. It is difficult to determine the failure probability of components in many kinds of complex systems, such as landing gear retraction systems and large-scale space-borne antennae This limits the application of the probabilistic model-based fault tree method in complex engineering applications. Based on the advantages of the universal grey number method, a new method for solving the reliability of the top event of a fault tree is proposed in this paper to overcome the shortcomings of the existing nonprobabilistic reliability method of interval operation. The proposed method complies with the conversion rule between the interval number and universal number, and the four arithmetic operations of the universal grey number

Interval Analysis of Simple System Fault Trees

Conclusions