Nonparametric control chart is an oncoming area from the statistical process control charts in recent years. Some researchers have developed various nonparametric control charts and investigated the detection capability of these charts. The major advantage of nonparametric control charts is that the underlying process is not specifically considered the assumption of normality or any parametric distribution. In this paper, two nonparametric exponentially weighted moving average (EWMA) control charts are based on nonparametric tests proposed by Sukhamte (1956) and Mood (1954), namely NE-S and NE-M control charts. Generally weighted moving average (GWMA) control charts are extended by utilizing design and adjustment parameters for monitoring the changes in the process variability, namely NG-S and NG-M control charts. Statistical performance is also investigated on NG-S and NG-M control charts with run rules. Moreover, Sensitivity analysis is performed to show the effects of design parameters under the nonparametric NG-S and NG-M control charts.