According to the GPS integrity monitoring based on INS, profound theoretical analysis and comparison were taken for residual chi-square test and the approach failure detection by means of Chebyshev's law of great number. Two concepts including detecting time delay and average deflection function which compare to threshold as the capabilitys of Fault Detecting were introduced for slope failure. A simulation study of two methods was done based on detection of step failure and slope failure. The simulation results prove the validity of two methods and the latter has some advantages.