Fault detection, with the characteristics of strong uncertainty and randomness, has always been one of the research hotspots in the field of aerospace. Considering that devices will inevitably encounter various unknown interference in the process of use, which greatly limits the performance of many traditional fault detection methods. Therefore, the main aim of this paper is to address this problem from the perspective of uncertainty and randomness of measurement signal. In information engineering, interval-valued neutrosophic sets (IVNSs), belief rule base (BRB), and Dempster-Shafer (D-S) evidence reasoning are always characterized by the strong ability in revealing uncertainty, but each has its drawbacks. As a result, the three theories are firstly combined in this paper to form a powerful fault detection algorithm. Besides, a series of innovations are proposed to improve the method, including a new score function based on p-norm for IVNSs and a new approach of calculating the similarity between IVNSs, which are both proved by authoritative prerequisites. To illustrate the effectiveness of the proposed method, flush air data sensing (FADS), a technologically advanced airborne sensor, is adopted in this paper. The aerodynamic model of FADS is analyzed in detail using knowledge of aerodynamics under subsonic and supersonic conditions, meanwhile, the high-precision model is established based on the aerodynamic database obtained from CFD software.