The usual practice in control charts is to assume that the chart parameters are known or accurately estimated from in-control historical samples and the data are free from outliers. Both these assumptions are not realistic in practice: a control chart may involve the estimation of process parameters from a very limited number of samples and the data may contain some outliers. In order to overcome these issues, in this paper, we develop an EWMA median chart with estimated parameters to monitor the mean value of a normal process. We study the Run Length properties of the proposed chart using a Markov Chain approach and the performance of the proposed chart is compared to the EWMA median chart with known parameters. Several tables for the design of the proposed chart are given in order to expedite the use of the chart by practitioners. An illustrative example is also given along with some recommendations about the minimum number of initial subgroups m for different sample sizes n that must be collected for the estimation of the parameters so that the proposed chart has identical performance as the chart with known parameters. From the results we deduce that a) there is a large difference between the known and estimated parameters cases unless the initial number of subgroups m is large and b) the difference between the known and estimated parameters cases can be reduced by using dedicated
The performance of the cumulative sum (CUSUM) control chart for the mean when measurement error exists is investigated. It is shown that the CUSUM chart is greatly affected by the measurement error. A similar result holds for the case of the CUSUM chart for the mean with linearly increasing variance. In this paper, we consider multiple measurements to reduce the effect of measurement error on the charts performance. Finally, a comparison of the CUSUM and EWMA charts is presented and certain recommendations are given.
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