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

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.