  The task of monitoring for a change in the mean of a sequence of Bernoulli
random variables has been widely studied. However most existing approaches make
at least one of the following assumptions, which may be violated in many
real-world situations: 1) the pre-change value of the Bernoulli parameter is
known in advance, 2) computational efficiency is not paramount, and 3) enough
observations occur between change points to allow asymptotic approximations to
be used. We develop a novel change detection method based on Fisher's Exact
Test which does not make any of these assumptions. We show that our method can
be implemented in a computationally efficient manner, and is hence suited to
sequential monitoring where new observations are constantly being received over
time. We assess our method's performance empirically via using simulated data,
and find that it is comparable to the optimal CUSUM scheme which assumes both
pre- and post-change values of the parameter to be known.
