Power of the scan statistic in detecting a changed segment in a Bernoulli sequence

Fu & Curnow (1990) derive recursive equations to find the level of significance and power of a likelihood ratio test for a changed segment of specified length, based on the scan statistic, the maximum number of successes within the specified length. Their method is computationally feasible for segment lengths of 20 or less. We present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for very large segment lengths. We also evaluate power when the duration of the increased length used in the test statistic does not correspond to the actual length.