Existing fault detection algorithms based on evidence theory typically assume that the evidence is independent. However, this assumption is often difficult to satisfy in practical engineering, especially when data sources are affected by complex interference environment, leading to significant discrepancies between theoretical analysis and actual results. In response to the above problems, a fault detection algorithm based on evidential reasoning with dependent evidence under complex interference environment is proposed. Initially, the evidence reliability is used to determine the evidence fusion sequence within a weighted model, reducing the uncertainty of fusion results caused by complex disturbances. Subsequently, considering the correlation of non-independent evidence in the evidence fusion stage, the maximum information coefficient is calculated to evaluate the degree of correlation between evidence. Furthermore, the dependence discounting factor is calculated based on the dependence coefficient of the evidence and incorporated into evidential reasoning rule. Lastly, considering the complex interference characteristics of data sources, a two-layer evidence decision-making mechanism inspired by boosting methods in statistical learning is designed to compute the final fault detection result. The feasibility and efficacy of the proposed algorithm are demonstrated through a fault detection experiment of aviation electromagnetic relays. Compared with existing methods, the advantage of the proposed algorithm is that it relaxes the requirement for independence of evidence, which is especially suitable for engineering environments that are subject to greater noise interference.