Chi-square Control Charts with Runs Rules

• Published in: Methodology and computing in applied probability 2011-12, Vol.13 (4), p.657-669
• Main Authors: Rakitzis, Athanasios C., Antzoulakos, Demetrios L.
• Format: Article
• Language: English
• Subjects: Applied mathematics; Business and Management; Computation; Computer science; Control charts; Criteria; Economics; Electrical Engineering; Life Sciences; Markov analysis; Mathematical analysis; Mathematical models; Mathematics and Statistics; Monitoring; Probability; Rule based; Statistics; Studies; Vectors (mathematics)
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-010-9178-7

The Hotelling’s χ 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 χ 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 χ 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.