In industrial processes, the multitude of sensors requires high reliability, yet traditional routine inspection methods for assessing their health status are not only time-consuming and labor-intensive but also fail to meet the demands for sensor intelligence development. To address this issue, a sensor self-diagnostic design method based on the statistical correlation of measurement data is proposed. This method establishes statistical relationship models using sensor measurement data and utilizes auto-encoders to extract features from sensor data and encode them in binary form. Considering both statistically independent and correlated situations of sensor measurement data, a statistical model for independent diagnosis is established by introducing fault detection probability and false alarm probability when reference values are available. In the absence of reference values, a multivariate statistical dependency model using the Gaussian Copula function is constructed to assess the correlation among parameters. Furthermore, relying on Bayesian theory, the model autonomously learns to ascertain the health status of sensors without reference values. The proposed method is demonstrated using a nickel flash furnace system as an example. In both modes, the posterior probability of sensor fault detection reaches 0. 92, indicating that the parameters of the fault statistical model align with the modeling expectations. Experimental results confirm that the proposed method accurately identifies faulty sensors in the measurement system under both modes, thereby validating its effectiveness and feasibility.