In this paper, we present a multiple hypothesis based approach to test the performance of the receiver autonomous integrity monitoring (RAIM) fault detection and the corresponding integrity bound against multiple failures. In particular, we investigate the resistance of RAIM for the combined constellation of global positioning system (GPS) and Russian global orbiting navigation satellite system (GLONASS) against multiple faults, based on the proposed method. This paper evaluates the exact probability of missed detection (PMD) under each failure, and we compare this PMD to the requirement for single failure (i.e., 10-4), as in lines with the proposed GPS/GLONASS MOPS test procedures. This is to check if the test procedures outlined in the MOPS could guarantee the required level of integrity even for multiple failures. It is shown that the maximum PMD for a pair of faults is approximately 10-2 when the test procedures and the corresponding assumptions from the MOPS are applied. Also, we compute total probability of hazardous misleading information (PHMI) by accounting for several fault hypotheses, including GLONASS constellation fault, and compare it with the integrity risk requirement of 10-7. The maximum PHMI for multiple satellite failures goes up to approximately 2 • 10-8 when the newly proposed methodology is applied.