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Abstract
Nonparametric control charts provide a robust alternative in practice when the form of the underlying distribution is unknown. Nonparametric CUSUM (NPCUSUM) charts blend the advantages of a CUSUM with that of a nonparametric chart in detecting small to moderate shifts. In this paper, we examine efficient design and implementation of Phase II NPCUSUM charts based on exceedance (EX) statistics, called the NPCUSUM-EX chart. We investigate the choice of the order statistic from the reference (Phase I) sample that defines the exceedance statistic. We see that choices other than the median, such as the 75th percentile, can yield improved performance of the chart in certain situations. Furthermore, observing certain shortcomings of the average run-length, we use the median run-length as the performance metric. The NPCUSUM-EX chart is compared with the NPCUSUM-Rank chart based on the popular Wilcoxon rank-sum statistic. We also study the choice of the reference value, k, of the CUSUM charts. An illustration with real data is provided.
Acknowledgements
This research was supported in part by the SARCHI (South African Research Chairs Initiative) at the University of Pretoria awarded to the second author.
Funding
Dr Graham would like to acknowledge the financial support provided by the South African National Research Foundation under the Thuthuka programme: TTK20100724000013247, Grant number: 76219.
Notes
1. The reference sample size affects the performance of the Phase II chart; see Appendix B of Mukherjee, Graham, and Chakraborti (Citation2013) for details.
2. Recall that