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 (ARL), we use the
median run-length (MRL) as the performance metric. The NPCUSUM-EX chart is compared with the
NPCUSUM-Rank chart proposed by Li et al. (2010) 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.
