CUSUM

Example cusum1

CUSUM (Cumulative Sum Control Chart) is a type of control chart used in statistical quality control to monitor small shifts in the process mean. It is particularly effective for detecting small and persistent changes in the process.

Overview

CUSUM charts are used to monitor the cumulative sum of deviations from a target value. Unlike traditional Shewhart control charts, which only consider the most recent data point, CUSUM charts take into account the history of the process, making them more sensitive to small shifts.

History

The CUSUM method was first introduced by E. S. Page in 1954. It has since become a widely used tool in various industries, including manufacturing, healthcare, and finance.

Methodology

The CUSUM chart is based on the cumulative sum of deviations from the target value. The cumulative sum is calculated as follows:

S_i = max(0, S_{i-1} + (X_i - \mu_0 - k))

where:

• S_i is the cumulative sum at the i-th observation
• X_i is the i-th observation
• \mu_0 is the target value
• k is the reference value or allowable slack

The process is considered out of control if the cumulative sum exceeds a predetermined threshold.

Applications

CUSUM charts are used in various applications, including:

• Manufacturing: Monitoring production processes to detect shifts in the mean.
• Healthcare: Tracking patient outcomes to identify changes in treatment effectiveness.
• Finance: Monitoring financial metrics to detect shifts in performance.

Advantages

• High sensitivity to small shifts in the process mean.
• Ability to detect persistent changes over time.
• Useful for processes with low variability.

Disadvantages

• More complex to implement compared to traditional control charts.
• Requires a larger amount of historical data for accurate monitoring.

Related Pages

• Control chart
• Statistical process control
• Shewhart control chart
• E. S. Page

See Also

• Manufacturing
• Healthcare
• Finance