Abstract:
Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying
distribution is not known. A Phase II nonparametric CUSUM chart based on the exceedance statistics, called
the exceedance CUSUM chart, is proposed here for detecting a shift in the unknown location parameter of a
continuous distribution. The exceedance statistics can be more efficient than rank-based methods when the
underlying distribution is heavy-tailed and/or right-skewed, which may be the case in some applications,
particularly with certain lifetime data. Moreover, exceedance statistics can save testing time and resources as
they can be applied as soon as a certain order statistic of the reference sample is available. Guidelines and
recommendations are provided for the chart’s design parameters along with an illustrative example. The inand
out-of-control performance of the chart are studied through extensive simulations on the basis of the
average run-length (ARL), the standard deviation of run-length (SDRL), the median run-length (MDRL) and
some percentiles of run-length. Further, a comparison with a number of existing control charts, including the
parametric CUSUM X chart and a recent nonparametric CUSUM chart based on the Wilcoxon rank-sum
statistic, called the rank-sum CUSUM chart, is made. It is seen that the exceedance CUSUM chart performs
well in many cases and thus can be a useful alternative chart in practice. A summary and some concluding
remarks are given.
