A statistically adaptive sampling policy to the Hotelling's T² control chart: Markov chain approach

ABSTRACT

We present an alternative sampling scheme for the Hotelling's T² control chart with variable parameters (VP T²) which allows the sampling interval h, the sample size n, and control limit k to vary between minimum and maximum values while keeping the warning line fixed over time. Our method uses only one measurement scale to overcome the difficulties of using two scales in practice. Later, we demonstrate the merits of the method in terms of its performance in detecting small-to-moderate shifts and its ease of application.

KEYWORDS:

• Adjusted average time to signal (AATS)
• Genetic algorithm (GA)
• Hotelling's T² control chart
• Multivariate control chart
• Variable parameters (VP)

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P30

Acknowledgment

We also would like to acknowledge the anonymous reviewers, the editor, and editor in chief, all of whom helped us to improve this article.

Funding

We thank Bu-Ali Sina University, Hamedan, Iran and National Fund for Scientific Research (FNRS) organization, Brussels, Belgium, that financially supported this research project.