Plant-wide oscillations are common in many industrial processes. During the past few years, various methods have been proposed for the detection of plant-wide oscillations, including methods based on the autocorrelation function, the independent components analysis (ICA) and the spectral envelope. This article is aimed at understanding the advantages and limitations of the available methods using simulated data sets. The ICA based method is also improved by deriving approaches for determining the number of dominant ICs and for differentiating between oscillatory and non-oscillatory ICs.