The properties of a first-order, constant variance, dynamic linear model when monitoring ani.i.d.process are used to develop a framework for monitoring processes under startup conditions. Under stationary conditions, the statistic used for updating the estimate of the posterior mean of the process is just the exponentially weighted moving average (EWMA) control chart statistic. As such, an adaptation of the EWMA chart, referred to within as a dynamicEWMA chart, is proposed for monitoring short production runs. The model is driven by a specification of a prior distribution in the mean and variance of the process. Simple approximations are developed for the posterior estimates of the model parameters to enable its use by shop floor personnel. It is based upon specifications in the sensitivity of the control chart procedure to special cause phenomena when the chart is operated in its stationary phase. Ani.i.d.process is simulated to determine the required control chart standard deviation multiplier to achieve an in-control average run length (ARL) of 500. The results of simulation runs of 5000 replicates are evaluated for a range of settings of the EWMA weighting factor.