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In this letter, we present a novel instance of the stochastic resonance effect in sequential detection. For a general binary hypotheses sequential detection problem, the detection performance is evaluated in terms of the expected sample size under both hypotheses. Improvability conditions are established for an injected noise to reduce at least one of the expected sample sizes for a sequential detection system using stochastic resonance. The optimal noise is also determined under such criteria. An illustrative example is presented where performance comparisons are made between the original detector and different noise modified detectors.