The traditional exponentially weighted moving average (EWMA) control chart is based on the assumption of normality. Its lack of real-time feedback and adaptive ability is viewed as a limitation in practical process quality monitoring. A nonparametric adaptive chart called the WSR-SRA-AEWMA chart was proposed. It is built by combining the Wilcoxon sign-rank method with the sliding rotation algorithm (SRA). The chart was designed to overcome the weaknesses of traditional charts in distributional assumptions and response sensitivity. The average run length (ARL) and the standard deviation of run length (SDRL) were evaluated by Monte Carlo simulation. These indicators were used to optimize the chart parameters. Finally, extrusion-process data from a polyethylene (PE) pipe manufacturer were analyzed. Three quality characteristics were used: outer diameter t, wall thickness d, and out-of-roundness r. The WSR-SRA-AEWMA chart was compared with the traditional EWMA chart and the rank-sum control chart (RSCC). The results demonstrate that the proposed method offers superior adaptability and detection performance compared to traditional control charts.