Chi-square Control Charts with Runs Rules

The Hotelling's chi(2) control chart is one of the most widely used multivariate charting procedures for monitoring the vector of means of several quality characteristics. As a Shewhart-type control chart, it incorporates information pertaining to most recently inspected sample and subsequently it is relatively insensitive in quickly detecting small magnitude shifts in the process mean vector. A popular solution suggested to overcome this handicap was the use of runs and scans rules as criteria to declare a process out-of-control. During the last years, the examination of Hotelling's chi(2) control charts supplemented with various runs rules has attracted continuous research interest. In the present article we study the performance of the Hotelling's chi(2) control chart supplemented with a r-out-of-m runs rule. The new control chart demonstrates an improved performance over other competitive runs rules based control charts.