This paper introduces a method to compute an upper bound on the integrity risk of cycle resolution in the presence of bounded measurement errors and faults. In high accuracy applications such as shipboard landing and autonomous airborne refueling, carrier phase cycle ambiguities must be estimated and resolved as integers (or 'fixed ambiguities'). In applications that also demand high integrity, the cycle resolution process must comply with a fault-free integrity risk requirement. Under normal error conditions, fault-free integrity risk can readily be quantified using existing cycle resolution methods; this is true even in the presence of known measurement biases. However, evaluating the integrity risk of a cycle resolution process under fault hypotheses has not yet been addressed. In the case of rare-event measurement faults such as satellite failures and atmospheric anomalies, the magnitude of the fault is never exactly known, but it can often be bounded. The bound can either be a result of a monitor's minimum detectable error, from extensive data analysis, or even from physical limitation. In this paper, we develop a method to account for these bounded errors in the computation of the integrity risk for navigation systems that rely on fixed carrier phase cycle ambiguities.