This article develops a tight integrity risk bound for residual-based (RB) advanced receiver autonomous integrity monitoring (ARAIM). ARAIM measurement models include nominal biases accounting for unknown but bounded errors, and faults of unbounded magnitude. In RB methods, upper bounding the integrity risk requires that one finds the worst-case directions of both the multisatellite fault vector and of the all-in-view nominal bias vector. Previous methods only account for the worst-case fault direction assuming zero nominal bias. To address this issue, in this article, we derive a new bounding method in parity space. The method establishes a direct relationship between mean estimation error and RB test statistic noncentrality parameter, which accounts for both faults and nominal errors. ARAIM performance is evaluated to quantify the improvement provided by the proposed method over previous approaches.