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Go Deeper: Cumulative Sum Charts Can Detect Small Shifts in a Process

Cusum charts can detect process shifts more rapidly than the XmR or XbarR. If a trend develops, it's evidence that the process has shifted.

Example of a Cusum Chart Created by QI Macros Add-in for Excel

A Cusum Chart consists of:

• A target which is either provided by you or calculated as the mean of your data.
• Upper Cusum Limit and Lower Cusum Limit lines.
• C+ and C- lines which represent the cumulative sum of deviations of successive sample means from a target. Use these lines to determine if your process is shifting.

Default values calculated in the Cusum Chart:

k (slack) = 1/2 of your StDev
(this is an estimated value, but can be changed)

FIR (Fast Initial Response) = 0
(This feature can be used to set an initial "head start" value to improve detection of an out-of-control condition at the start of the chart. If the process is in control, this initial head start has little effect; if the process is out of control, a signal will be given faster with a non-zero value than with a zero value)

h (threshold value or decision interval) = 4
(this determines how many StDev from the mean the Cusum Limits are set)

NOTE: Using h=4 or h=5 and k=.5 will generally provide a cusum that has good ARL properties (per Montgomery SPC 4th ed.)

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Compare a Cusum Chart with an EWMA Chart

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Compare a Cusum Chart with an Individual Moving Range Chart

Notice how the Cusum chart more quickly and clearly identifies the process shift.

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Learn More...

• Watch Cusum Chart video
• Cusum Chart Template
• Exponentially Weighted Moving Average EWMA charts

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