Improved chi-square control charts with weak-run rules

The chi-square control chart is one of the most popular multivariate charting techniques for monitoring the vector of means of several quality characteristics. During the last decades, runs rules have been supplemented in the design of the chi-square control chart and they have significantly improved its performance. In this article, we introduce and study a chi-square control chart with supplementary weak-run rules, which improves the chart’s detection capability in the case of small and moderate process mean vector shifts. Our study also establishes new theoretical results regarding the waiting time for the first occurrence of an r-weak run in a sequence of binary trials.卡方控制图（chi-square control chart）是当前最常用的多元控制图技术之一，用于监控多项质量特性的均值向量。近数十年来，游程规则（runs rules）被补充应用于卡方控制图的设计中，显著提升了该控制图的性能表现。本文提出并研究了一种搭载附加弱游程规则的卡方控制图，该方案可有效提升控制图在过程均值向量出现小幅或中幅偏移时的异常检测能力。本研究还针对二元试验序列中r次弱游程首次出现的等待时间，推导得到了全新的理论结果。