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I am trying to apply SPRT on a vector signal (of residual) for detecting faults occurring in the sensors' measurement of an aircraft. The vector signal contains measurements from five different sensors of the aircraft. So I wanted to inquire whether the SPRT is to be applied separately for each sensor signal, each having a different set of parameters for the test?

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Yes, for N stationary time series, or for N residuals from which the serial correlation has been filtered, it's necessary to apply N univariate SPRTs in parallel for anomaly detection.

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