Abstract
In failure detection, we have two incompatible demands: One is the high reliability for detection, the other is the short mean detection time. That is, if the mean detection time is long, the loss due to delays of detection will be large. On the other hand, if the mean detection time is short, the loss due to false alarms will be large. In this paper, we consider an optimization problem of a failure detection system that balances the two incompatible demands described above.
Here, as a detection method, the modified Wald's SPRT is used. This method, which works well for detection of failures or parameter changes, uses a likelihood ratio computed from a sequence of observation data with noise.
A proposed problem is as follows: find the optimal mean time T between two false alarms to minimize the mean performance deterioration of the given system, when the performance deterioration ratios for the false alarm and the miss alarm are known. A solution for this problem is given and finally a simple numerical example is given.
