In Experimental Fluid Dynamics (EFD), the finite length of e.g. a towing tank induces start-up effects, end effects and random uncertainty in the mean value of a measurement signal. The same happens to signals generated by Computational fluid Dynamics (CFD), where the finite computation length is influenced by start-up effects and random uncertainty occurs (also known as the 'aleatory uncertainty' in CFD communities).To verify the stationarity of a signal, a new technique called 'Transient Scanning Technique' or TST is presented. This technique is a practical and simple tool which is based on the behaviour of the random uncertainty of the mean. It allows the user to check whether the signal approaches a stationary state or not. Further, it identifies trends (or transients) in signals. Using this information, start-up and end effects can be identified and removed from the signal. With the remaining signal, the random uncertainty of the mean can accurately be estimated from a single realisation. In this paper the TST is thoroughly explained and its application on EFD and CFD results is demonstrated.