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.