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 (ARLIN). 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.

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Because of digitalization, many organizations possess large datasets. Furthermore, measurement data are often not normally distributed. However, when samples are sufficiently large, the central limit theorem may be used for the sample means. In this article, we evaluate the use of the central limit theorem for various distributions and sample sizes, as well as its effects on the performance of a Shewhart control chart for these large non‐normally distributed datasets. To this end, we use the sample means as individual observations and a Shewhart control chart for individual observations to monitor processes. We study the unconditional performance, expressed as the expectation of the in‐control average run length (ARL), as well as the conditional performance, expressed as the probability that the control chart based on estimated parameters will have a lower in‐control ARL than a specified desired in‐control ARL. We use recently developed factors to correct the control limits to obtain a specified conditional or unconditional in‐control performance. The results in this paper indicate that the control chart should be applied with caution, even with large sample sizes.

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One of the most common applications in statistical process monitoring is the use of control charts to monitor a process mean. In practice, this is often done with a Shewhart X chart along with a Shewhart R (or an S) chart. Thus two charts are typically used together, as a scheme, each using the 3-sigma limits. Moreover, the process mean and standard deviation are often unknown and need to be estimated before monitoring can begin. We show that there are three major issues with this monitoring scheme described in most textbooks. The first issue is not accounting for the effects of parameter estimation, which is known to degrade chart performance. The second issue is the implicit assumption that the charting statistics are both normally distributed and, accordingly, using the 3-sigma limits. The third issue is multiple testing, since two charts are used, in this scheme, at the same time. We illustrate the deleterious effects of these issues on the in-control properties of the ( , ) XR charting scheme and present a method for finding the correct charting constants taking proper account of these issues. Tables of the new charting constants are provided for some commonly used nominal in-control average run-length (ICARL 0 ) values and different sample sizes. This will aid in implementing the ( , ) XR charting scheme correctly in practice. Examples are given along with a summary and some conclusions.