The X̄ chart works well under the assumption of random sampling from infinite populations. However, many process monitoring scenarios may consist of random sampling from finite populations. A modified X̄ chart is proposed in this article to solve the problems encountered by the standard X̄ chart when samples are drawn from finite populations.
Khoo, Michael B. C.
"A Modified X̄ Control Chart for Samples Drawn from Finite Populations,"
Journal of Modern Applied Statistical Methods: Vol. 6
, Article 24.
Available at: http://digitalcommons.wayne.edu/jmasm/vol6/iss2/24