Design of EWMA-type control chart

Abstract

A control chart is typically examined based on the overall performance. This is crucial, as it will influence the final decision on the selection of a control chart. For this reason, the application of average run length (ARL) has been identified as the standard performance metric. In order to calculate ARL, practitioners must determine the size of the process shift in advance. Nevertheless, in practice, the process shift size cannot be predetermined, as practitioners may not have the requisite information associated with the process. Hence, in this work, the expected average run length (EARL) is employed as a performance metric for the unknown shift size in a process. This work evaluates the performance of a memory-type control chart, i.e. exponentially weighted moving average median (EWMA median) chart, with respect to ARL and EARL. The results indicate that, as long as the deterministic shift size is within the range of the process shift size, the chart’s performance is nearly the same, regardless of the use of the optimal pair based on minimizing ARL or EARL.