cumulative sum control chart 

Synonym: CUSUM chart
https://doi.org/10.1351/goldbook.08071
Control chart where the cumulative sum of deviations of successive measured quantity values from a reference quantity value is plotted to detect shifts in the level of the measurand.
Notes:
  1. The ordinate of each plotted point represents the algebraic sum of the previous ordinate and the most recent deviation from the reference, target, or control value.
  2. The best discrimination of changes in the level is achieved when the reference quantity value is equal to the overall mean value.
  3. The chart can be used for control, diagnostic, or predictive purposes.
  4. When used for process control, it can be interpreted graphically using a mask (for example, V-mask) superimposed on the graph. An out-of-control criterion is when the path of the cumulative sum intersects or touches the boundary of the mask.
  5. More suited to spreadsheet analysis, the following quantities are calculated for N measured quantity values xi(i=1;…,N) Shi(i)=max(0,Shi(i−1)+xi−μ−k); Shi(0)=0 Slo(i)=max(0,Slo(i−1)−xi+μ−k); Slo(0)=0. μ is a suitably chosen target value and k is a reference quantity value such that only shifts away from the target value greater than k will add to the cumulative sum. k is usually taken as half the shift in the process mean that is required to be detected divided by the standard deviation (σ) obtained under repeatability conditions of measurement. An out-of-control criterion is when Shi(i) or Slo(i) becomes greater than a limiting value h (usually h=4σ). (Note that the reference quantity value k is not a coverage factor).
  6. CUSUM charts are particularly sensitive to reveal a small measurement bias.
Source:
PAC, 2021, 93, 997. (Metrological and quality concepts in analytical chemistry (IUPAC Recommendations 2021)) on page 1024 [Terms] [Paper]
Citation: 'cumulative sum control chart' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.08071 RIS BibTex EndNote
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