Evaluation of the economic statistical design of the multivariate T² control chart with multiple variable sampling intervals scheme: NSGA-II approach

Abstract

The economic and statistical merits of a multiple variable sampling intervals scheme are studied. The problem is formulated as a double-objective optimization problem with the adjusted average time to signal as the statistical objective and the expected cost per hour as the economic objective. Bai and Lee's [An economic design of variable sampling interval ¯X control charts. Int J Prod Econ. 1998;54:57–64] economic model is considered. Then we find the Pareto-optimal designs in which the two objectives are minimized simultaneously by using the non-dominated sorting genetic algorithm. Through an illustrative example, the advantages of the proposed approach are shown by providing a list of viable optimal solutions and graphical representations, which indicate the advantage of flexibility and adaptability of our approach.

Keywords:

• multivariate T² control chart
• multi-objective optimization
• economic statistical design
• NSGA-II algorithm
• variable sampling intervals scheme

Acknowledgements

We also would like to acknowledge and extend our heartfelt gratitude to Prof. Erwin Saniga, the anonymous reviewers, the Editor and Editor in chief, all of whom helped us to improve the last version of this paper.

Additional information

Funding

We thank the Islamic Azad University, Hamedan Branch, Hamedan, Iran and National Fund for Scientific Research (FNRS) organization, Brussels, Belgium for the financial support. Alireza Faraz acknowledges financial support from F.R.S.-FNRS (postdoctoral researcher grant from ‘Fonds de la Recherche Scientifique-FNRS’, Belgium) and from IAP research network P7/06 of the Belgian Government (Belgian Science Policy)