基于数据幂变换的EEWMA高质量过程控制

EEWMA High-Quality Process Control Based on Data Power Transformation

摘要: 针对高质量过程的改进或恶化的监控问题，以服从指数分布的事件间隔时间(TBE)为监控指标，通过对TBE样本数据进行幂次为3.6的幂变换使其近似服从正态分布以改善分布的偏态性，在图统计量中同时考虑TBE的历史、当前以及最新变化信息以提高对TBE均值变化的敏感度，开发了基于数据幂变换的扩展指数加权移动平均控制图(PT-based EEWMA)，实现了对过程恶化、改进的监控。数值实验表明，相比于现有基于幂变换的EWMA、DEWMA控制图，PT-based EEWMA控制图在监测TBE均值偏移时，对不同方向、大小的偏移均表现出更好的ARL性能。更进一步，通过数值实验分析了真实分布为威布尔分布时，分布的形状、尺度参数的变化对指数分布下PT-based EEWMA控制图性能的影响。结果表明，该控制图对威布尔分布也具有一定的稳健性。

Abstract: Aiming at the problem of improvement or deterioration of high-quality processes, a power trans-formation-based extended exponentially weighted moving average control chart (PT-based EEWMA) is proposed, in which introducing the time between events (TBE) that follows an exponential dis-tribution as the monitoring indicator, transforming the TBE sample data with a power 3.6 to weak-en the skewness of its original distribution, and integrating the historical, current, and latest changes information of TBE in the control chart statistic to raise the sensitivity to shifts in the mean value of TBE, and at last the monitoring of process deterioration and improvement is achieved. Nu-merical experiments show that compared with the existing EWMA and DEWMA control charts, the proposed PT-based EEWMA control chart presents a better ARL performance for TBE mean shifts in different directions and sizes. Furthermore, the influence of the shape and scale parameters of the real distribution on the performance of PT-based EEWMA control chart under exponential distribu-tion is analyzed through numerical experiments. The results show that the control chart is also ro-bust to Weibull distribution.