Wilcoxon-type rank-sum control charts based on progressively censored reference data

Abstract

In this article, we introduce a new distribution − free Shewhart − type control chart implementing a modified Wilcoxon-type rank sum statistic based on progressive Type-II censoring reference data. The proposed chart is also a tool for monitoring the incomplete data, because the censoring scheme applied allows the protection of experimental units at an early stage of the testing procedure. The setup of the new nonparametric control chart is presented in detail, while its operating characteristic function is studied. Explicit formulae for the evaluation of Alarm Rate and Average Run Length values for both in-control and out-of-control situations are established. A numerical study carried out depicts the performance and robustness of the proposed control chart. For illustration purposes, a practical example is also discussed.

Keywords:

• Nonparametric control charts
• Type-II progressive censoring
• Lehmann alternatives
• statistical process control
• maximal Wilcoxon rank-sum statistic

Acknowledgments

The author is grateful to the Editor-in-Chief and two anonymous referees for their constructive comments and suggestions that lead to a substantial improvement of the paper.