Sequential probability ratio tests (SPRTs) are applied to the monitoring of nuclear power reactor signals. The theory of SPRTs applied to correlated data that have an unknown distribution is very incomplete. Unfortunately, a common problem regrading the application of sequential methods to reactor variables is that the variables are often contaminated with noise that is either non-Gaussian or serially correlated (or both). A Fourier series approximation can be used to remove much of the correlation in the data. This method is relatively simple to implement but has the desirable property of reducing correlation, thereby allowing the assumption of Gaussian, independent data to hold more readily. Delayed neutron signal data and reactor coolant pump data are analyzed. The theory has been validated by extensive testing with data from the Experimental Breeder Reactor II. The use of SPRT techniques as decision aids in two artificial intelligence-based expert systems for surveillance and diagnosis applications in nuclear reactors is also discussed.