In quantitative discrete-event simulation, the initial transient phase can cause bias in the estimation of steady-state performance measures. Methods for detecting and truncating this phase make calculating accurate estimates from the truncated sample possible, but no methods proposed in the literature have proved to work universally in the sequential online analysis of output data during simulation. This report proposes a new automated truncation method based on the convergence of the cumulative mean to its steady-state value. The method uses forecasting techniques to determine this convergence, returning a truncation point when the cumulative mean time-series becomes sufficiently horizontal and flat. Values for the method’s parameters are found that adequately truncate initialisation bias for a range of simulation models. The new method is compared with the sequential MSER-5 method, and shows to detect the onset of steady-state more effectively and consistently for almost all simulation models that are tested. This rule thus appears to be a good candidate as a robust sequential truncation method and for implementation in sequential simulation research packages such as Akaroa2.