  For the most popular sequential change detection rules such as CUSUM, EWMA,
and the Shiryaev-Roberts test, we develop integral equations and a concise
numerical method to compute a number of performance metrics, including average
detection delay and average time to false alarm. We pay special attention to
the Shiryaev-Roberts procedure and evaluate its performance for various
initialization strategies. Regarding the randomized initialization variant
proposed by Pollak, known to be asymptotically optimal of order-3, we offer a
means for numerically computing the quasi-stationary distribution of the
Shiryaev-Roberts statistic that is the distribution of the initializing random
variable, thus making this test applicable in practice. A significant
side-product of our computational technique is the observation that
deterministic initializations of the Shiryaev-Roberts procedure can also enjoy
the same order-3 optimality property as Pollak's randomized test and, after
careful selection, even uniformly outperform it.
