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A memory-type control chart utilizes previous information for chart construction. An example of a memory-type chart is an exponentially-weighted moving average (EWMA) control chart. The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts. Meanwhile, the EWMA median chart is robust against outliers. In light of this, the economic model of the EWMA and EWMA median control charts are commonly considered. This study aims to investigate the effect of cost parameters on the out-of-control average run length (ARL1) in implementing EWMA and EWMA median control charts. The economic model was used to compute the ARL1 parameter. The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis. When the input parameters change based on a predetermined percentage, the ARL1 is affected. According to the results of the EWMA chart, nine input parameters had an effect and five input parameters had no effect on the ARL1 parameter. Further, only seven of the 14 input parameters had an effect on the ARL1 of the EWMA median chart. However, the effect of each input parameter on the ARL1 was different. Moreover, the ARL1 for the EWMA median chart was smaller than the EWMA chart. This analysis is crucial to observe and determine the input parameters that have a significant impact on the ARL1 of the EMWA and EWMA median control charts. Hence, practitioners can obtain an overview of the influence of the input parameters on the ARL1 when implementing the EWMA and EWMA median control charts. [ABSTRACT FROM AUTHOR]