The variable parameters T2 chart with run rules

• Published in: Statistical papers (Berlin, Germany) Vol. 55; no. 4; pp. 933 - 950
• Main Authors: Faraz, Alireza, Celano, Giovanni, Saniga, Erwin, Heuchenne, C., Fichera, S.
• Format: Journal Article Web Resource
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2014; Springer Science & Business Media B.V
• Subjects: Business & economic sciences; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Genetic algorithms (GA); Hotelling’s T2 Control chart; Insurance; Management; Markov chain; Mathematics and Statistics; Méthodes quantitatives en économie & gestion; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Quantitative methods in economics & management; Regular Article; Run rules; Sciences économiques & de gestion; Statistics; Statistics for Business; Variable parameters (VP); Markov chain; Run rules; Control chart; Genetic algorithms (GA); Hotelling’s; Variable parameters (VP)
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-013-0537-7

The Hotelling’s
T
2
control chart with variable parameters (
VP
T
2
)
has been shown to have better statistical performance than other adaptive control schemes in detecting small to moderate process mean shifts. In this paper, we investigate the statistical performance of the
VP
T
2
control chart coupled with run rules. We consider two well-known run rules schemes. Statistical performance is evaluated by using a Markov chain modeling the random shock mechanism of the monitored process. The in-control time interval of the process is assumed to follow an exponential distribution. A genetic algorithm has been designed to select the optimal chart design parameters. We provide an extensive numerical analysis indicating that the
VP
T
2
control chart with run rules outperforms other charts for small sizes of the mean shift expressed through the Mahalanobis distance.