On Threshold Optimization in Fault Tolerant Systems
Fault tolerant systems are considered, where a nominal system is
monitored by a fault detection algorithm, and the nominal system is
switched to a backup system in case of a detected fault. Conventional
fault detection is in the classical setting a trade-off between
detection probability and false alarm probability. For the considered
fault tolerant system, a system failure occurs either when the nominal
system gets a fault that is not detected, or when the fault detector
signals an alarm and the backup system breaks down. This means that
the trade-off for threshold setting is different and depends on the
overall conditions, and the characterization and understanding of this
trade-off is important. It is shown that the probability of system
failure can be expressed in a general form based on the probability of
false alarm and detection power, and based on this form the influence
ratio is introduced. This ratio includes all information about the
supervised system and the backup system that is needed for the
threshold optimization problem. It is shown that the influence ratio
has a geometrical interpretation as the gradient of the receiver
operating characteristics (ROC) curve at the optimal point, and
furthermore, it is the threshold for the optimal test quantity in
important cases.
Fredrik Gustafsson, Jan Åslund, Erik Frisk, Mattias Krysander and Lars Nielsen
IFAC World Congress,
2008
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