Guaranteed in-control performance of the EWMA chart for monitoring the mean

Research on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in-control average run-length (ARL_IN). Recent research has highlighted the high variability in the in-control performance of these charts. This has led to the recommendation of studying of the conditional in-control average run-length (CARLIN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARLIN distribution and the exceedance probability criterion (EPC). The CARLIN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in-order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and Graphs of the adjusted constants are provided. An in-control and out-of-control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in-control and out-of-control performance tradeoff can be made to improve performance.