A distribution-free control chart for the joint monitoring of location and scale

A. Mukherjee, S. Chakraborti*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

68 Citations (Scopus)


Traditional statistical process control for variables data often involves the use of a separate mean and a standard deviation chart. Several proposals have been published recently, where a single (combination) chart that is simpler and may have performance advantages, is used. The assumption of normality is crucial for the validity of these charts. In this article, a single distribution-free Shewhart-type chart is proposed for monitoring the location and the scale parameters of a continuous distribution when both of these parameters are unknown. The plotting statistic combines two popular nonparametric test statistics: the Wilcoxon rank sum test for location and the Ansari-Bradley test for scale. Being nonparametric, all in-control properties of the proposed chart remain the same and known for all continuous distributions. Control limits are tabulated for implementation in practice. The in-control and the out-of-control performance properties of the chart are investigated in simulation studies in terms of the mean, the standard deviation, the median, and some percentiles of the run length distribution. The influence of the reference sample size is examined. A numerical example is given for illustration. Summary and conclusions are offered.

Original languageEnglish
Pages (from-to)335-352
Number of pages18
Issue number3
Publication statusPublished - Apr 2012
MoE publication typeA1 Journal article-refereed


  • Ansari-Bradley statistic
  • average run length
  • Lepage statistic
  • Monte Carlo simulation
  • nonparametric
  • Shewhart-Lepage chart
  • statistical process control
  • Wilcoxon statistic


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