Consequences of using the probability of a false alarm as the false alarm measure

• In systems for on-line detection of regime shifts, a process is continually observed. Based on the data available, we make repeated decisions such that when there is enough evidence of a change, an alarm is given. There is a risk of a false alarm and here two different ways of controlling the false alarms are compared: systems with a fixed average run length until the first false alarm, and systems with a fixed probability (<1) of any false alarm (fixed size). The effects of the two approaches are evaluated in terms of the timeliness of alarms. A system with a fixed size is found to have a drawback: the ability to detect a change deteriorates rapidly with the time of the change. Consequently, the probability of successful detection will tend to zero and the expected delay of a motivated alarm tends to infinity. This drawback is present even when the size is set to be very large (close to 1). Utility measures expressing the different costs for a false or a too late alarm are used in the comparison. How the choice of the best approach can be guided by the parameters of the process and the different costs of alarms is demonstrated. The technique is illustrated by a case study.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

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