The X control chart for monitoring process shifts in mean and variance

Mei Yang, Zhang Wu, Ka Man Lee, Michael B C Khoo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


Control charts are widely used in statistical process control (SPC) to monitor the quality of products or production processes. When dealing with a variable (e.g., the diameter of a shaft, the hardness of a component surface), it is necessary to monitor both its mean and variability (Montgomery 2009 [Montgomery, D.C., 2009. Introduction to statistical quality control. New York: John Wiley & Sons.]). This article studies and compares the overall performances of the X chart and the 3-CUSUM chart for this purpose. The latter is a combined scheme incorporating three individual CUSUM charts and is considered as the most effective scheme for detecting mean shift and/or standard deviation shift in current SPC literature. The results of the performance studies reveal two interesting findings: (1) the best sample size n for an chart is always n=1, in other words, the simplest X chart (i.e., the chart with n=1) is the most effective chart for detecting and/or; (2) the simplest X chart often outperforms the 3-CUSUM chart from an overall viewpoint unless the latter is redesigned by a difficult optimisation procedure. However, even the optimal 3-CUSUM chart is only slightly more effective than the X chart unless the process shift domain is quite small. Since the X chart is very simple to understand, implement and design, it may be more suitable in many SPC applications, in which both the mean and variance of a variable need to be monitored.
Original languageEnglish
Pages (from-to)893-907
Number of pages15
JournalInternational Journal of Production Research
Issue number3
Publication statusPublished - 1 Feb 2012
Externally publishedYes


  • CUSUM chart
  • quality control
  • Shewhart chart
  • statistical process control

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Management Science and Operations Research
  • Strategy and Management


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