In sequential change detection, existing performance measures differ
significantly in the way they treat the time of change. By modeling this
quantity as a random time, we introduce a general framework capable of
capturing and better understanding most well-known criteria and also propose
new ones. For a specific new criterion that constitutes an extension to
Lorden's performance measure, we offer the optimum structure for detecting a
change in the constant drift of a Brownian motion and a formula for the
corresponding optimum performance.Comment: Published in at http://dx.doi.org/10.1214/009053607000000938 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
