Distribution-free exceedance cusum control charts for location

A. Mukherjee*, M. A. Graham, S. Chakraborti

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

45 Citations (Scopus)


Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. A Phase II nonparametric cumulative sum (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 in- and out-of-control performances 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 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.

Original languageEnglish
Pages (from-to)1153-1187
Number of pages35
Issue number5
Publication statusPublished - 1 May 2013
MoE publication typeA1 Journal article-refereed


  • Binomial
  • CUSUM chart
  • Exceedance statistic
  • Markov chain
  • Nonparametric
  • Precedence statistic
  • Quality control
  • Robust
  • Simulation


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