This study presents a new Kalman-filter-based integrity monitoring algorithm that considers fault duration length a variable. The existing integrity monitoring algorithms that assumed a single fault duration with a constant prior probability were extended to account for the multiple hypotheses of fault duration with different prior probabilities. The methods for integrity risk computations were presented for both single and multiple cumulative innovation monitors. Performance analysis of the proposed method was carried out by applying it to a GNSS/INS attitude heading reference system. In this process, the prior probabilities of the fault hypotheses were modeled through Monte Carlo simulations. The results show that the heading integrity risk of the single-hypothesis approach can be reduced by a factor of 12 when applying the multi-hypothesis approach, and the heading integrity risk of the multi-hypothesis approach can be further reduced by a factor of 5 by using multiple monitors. The sensitivity analyses demonstrate that the integrity risk strongly depends on the quality of carrier phase measurements and decreases as a false alarm probability or alert limit increases.