In practical applications of statistical process control (SPC), the distribution in which the sample data follow often remains unknown. Non-parametric control charts are necessary in process monitoring in such cases. A triple generally weighted moving average (TGWMA) sign chart is proposed in this study for monitoring the process when the underlying distribution is unknown. Simulation is used to compare the performance of the TGWMA sign chart with the existing double generally weighted moving average (DGWMA) sign chart, for both steady state (SS) and zero state (ZS) cases. From the comparison, the TGWMA sign chart shows superior sensitivity in identifying small shifts in the process proportion for both ZS and SS cases. Lastly, we demonstrate the application of the TGWMA sign chart through a practical example and compare it to the DGWMA sign chart in detecting process shifts, further showing the effectiveness of using the TGWMA sign chart.