Based on Kalman filtering, multi-sensor navigation systems, such as the integrated GPS/INS system, are widely accepted to enhance the navigation solution for various applications. However, such integrated systems do not always provide robust and stable navigation solutions due to unmodelled measurements and system dynamic errors, such as faults that degrade the performance of Kalman filtering for such integration. Single fault detection methods based on least squares (snapshot) method were investigated extensively in the literature and found effective to detect the fault at either sensor level or integration level. However, the system might be contaminated b multiple faults simultaneously. Thus, there is an increased likelyhood that some of the faults may not be detected and identified correctly. This will degrade the accuracy of positioning. In this paper multiple fault test and reliability measures based on a snapshot method were implemented in both the measurement model and the predicted states model for use in a GPS/INS integration system. The influences of the correlation coefficients between fault test statistics on the performances of the faults test and reliability measures were also investigated. The results indicate that the multiple fault test and reliability measures can perform more effectively in the measurement model than the predicted states model due to weak geometric strength within the predicted states model