CUSUM Control Chart
Cumulative Sum (CUSUM) Control Chart · Also known as: cumulative sum chart, CUSUM control chart, Page's CUSUM, kümülatif toplam kontrol kartı
The cumulative sum (CUSUM) control chart, introduced by E. S. Page in 1954, monitors a process by accumulating the deviations of observations from a target value rather than judging each point in isolation. Because small persistent shifts add up over time, the running sum makes them visible far sooner than a Shewhart chart, making CUSUM the tool of choice for detecting small, sustained changes in the process mean.
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When to use it
Use a CUSUM chart when the priority is rapid detection of small, sustained shifts in the process mean — on the order of half a sigma to one and a half sigma — that a Shewhart chart would miss for many samples. It suits high-value or safety-critical processes, individual-measurement monitoring, and any setting where a slow drift must be caught early. It assumes a known in-control target and standard deviation and approximately independent observations, and it is tuned through k and h to a desired average run length. Because CUSUM is comparatively slow to react to very large, abrupt shifts, it is often run alongside a Shewhart chart, which excels at those; the EWMA chart is a close alternative with similar small-shift sensitivity.
Strengths & limitations
- Detects small, sustained shifts in the mean far faster than a Shewhart chart.
- Uses all past data through accumulation, giving high sensitivity to persistent drift.
- Tunable via k and h to a target average run length for a specific shift size.
- Effective for individual measurements, not only subgroups.
- Slower than Shewhart charts at detecting very large, abrupt shifts.
- Requires a reliable in-control target and standard deviation.
- Less intuitive to read and explain than a simple Shewhart chart.
- Sensitive to autocorrelation, which distorts the run-length properties.
Frequently asked
How does CUSUM differ from a Shewhart chart?
A Shewhart chart judges each point against fixed limits, so it reacts fast to large shifts but slowly to small ones. CUSUM accumulates deviations from target over time, giving it memory and making it much faster at detecting small, sustained shifts at the cost of slower response to large abrupt ones.
What do the parameters k and h mean?
k is the reference value or 'allowance', usually set to about half the shift (in sigma units) you want to detect; it keeps the cumulative sums from drifting on noise. h is the decision interval — the threshold the sums must cross to signal. Together they are chosen to achieve a target average run length.
Should I use CUSUM or EWMA?
Both are memory-based charts with similar sensitivity to small shifts. CUSUM is optimal for detecting a specific shift size it is tuned to; EWMA is slightly easier to design and interpret and degrades more gracefully across shift sizes. The choice is often a matter of convention and preference.
Sources
- Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100–115. DOI: 10.1093/biomet/41.1-2.100 ↗
- Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6th ed.). John Wiley & Sons. ISBN: 978-0-470-16992-6
How to cite this page
ScholarGate. (2026, June 2). Cumulative Sum (CUSUM) Control Chart. ScholarGate. https://scholargate.app/en/statistics/cusum-chart
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Attributes Control ChartStatistics↔ compare
- EWMA ChartStatistics↔ compare
- Sequential AnalysisStatistics↔ compare
- Shewhart Control ChartStatistics↔ compare