The start-up or initial transient problem arises in steady state, discrete-event simulation, where a selection of non-typical initial conditions introduces bias in simulated output sequences. One way of dealing with initialisation bias is to delete a portion of the output from the beginning of the run, to eliminate the effects of bias caused by these initial conditions. To make sure that the remaining observations represent steady state behaviour, it is safer to remove more than enough observations from the beginning of the run but only to an extent that not too many good observations are removed. This research focuses on the initial transient period and the proposed statistical tests for detecting its length. Our aim here is to find a statistical test that in addition to overestimating the length of the initial transient period it detects a length as accurately as possible (in finding a length as close to the one estimated by the theory).