Average Run Lengths of an Optimal Method of Detecting a Change in Distribution.

摘要

Suppose one accumulates independent observations from a certain process. Initially, the process is at State 0. At some unknown point in time something occurs (e.g., a breakdown ) which puts the process in State 1, and consequently the stochastic behavior of the observations changes. It is of interest to declare that a change took place (to raise an alarm) as soon as possible after its occurrence, subject to a restriction on the rate of false detections. It is assumed that the aforementioned observations are the only information one has about the process, and the problem is to construct a good detection scheme. Practical examples of this problem arise in areas such as health, quality control, ecological monitoring, etc. For instance, consider surveillance for congenital malformations in newborn infants. Under normal circumstances, the percentage of babies born with a certain type of malformation has a known value. Should something occur (such as an environmental change, the introduction of a new drug to the market, etc.) the percentage may increase. One would want to raise an alarm as quickly as possible after a change would have taken place, subject to an acceptable rate of false alarms.