What is a CUSUM chart?
Like control charts, CUSUM charts are used to plot data in time-series. The charts are meant to alert users to significant changes in process performance. CUSUM charts do not plot raw data values, averages, ranges or standard deviations. Instead, plot points on a CUSUM chart are data values roughly representative of the cumulatively summed, subgroup-to-subgroup deviations from a specified target or production mean. The primary advantage of the tabular CUSUM chart is that the chart is more sensitive to small changes in the mean, especially when compared with IX-MR control charts.
Why Use a CUSUM Chart?
Basically, it boils down to sensitivity. X̄ and Range and X̄ and S control charts are commonly understood, powerful process control tools. Their power lies in plotting average values which become more normally distributed as the subgroup size, n, increases. The larger the subgroup size, the more sensitive X̄ charts become in detecting significant shifts in the mean. Increasing control chart sensitivity is as simple as increasing subgroup size.
But not everyone has the luxury of creating large subgroups. Consider manufacturing organizations who specialize in short production runs or who rely on destructive testing to quantify product quality. In these cases, very little data is available, or it is cost-prohibitive to collect. Therefore, large subgroups are not an option.
If subgrouping cannot be leveraged, then an Individual X and Moving Range (IX-MR) control chart might seem like a good alternative to X̄ and Range control charts. However, because plotted points on IX charts are individual data values (not averages), the IX values are less sensitive to small changes in the overall mean, especially when compared with X̄ charts.
Another reason CUSUM charts are popular is their ability to mitigate risk. For example, consider companies who tempt catastrophe when critical data values stray too far away from production targets. These organizations cannot afford to wait until plot point falls outside +/-3σ control limits before generating an alarm. Instead, they need greater sensitivity to small process changes.
Each of the situations above indicates why CUSUM charts are useful. When small changes in the mean (1 – 1.5σ) must be identified and when very little data is available for process control purposes, the CUSUM chart is an excellent solution. As such, the CUSUM chart is popular in the aerospace, metallurgical, chemical and continuous processing industries.
How Are CUSUM Charts Created?
When compared with traditional control charts, the tabular CUSUM chart is unique, and certain parameters and statistics must be used in its creation.
| Parameter | Description |
| The plot point is used exclusively for plotting the upper line on the tabular CUSUM chart. The upper line is used for identifying changes in the process above the stated target value, . | |
| The point is used exclusively for plotting the lower line on the tabular CUSUM chart. The lower line is used for identifying changes in the process below the chosen target value, . | |
| Process Mean or Target value. | |
| Sample standard deviation, or Long Term (LT) standard deviation. | |
| The positive shift in Process Mean that the CUSUM chart is meant to detect, in standard deviation units. Typically between 0.5σ and 1.5σ. | |
| The negative shift in Process Mean that the CUSUM chart is meant to detect, in standard deviation units. Typically between 0.5σ and 1.5σ. | |
| The “Upper Reference” value specified for plotted Positive CUSUM line. Positive CUSUM values are accumulated only when the deviation from the target value exceeds specified K value. K value is half the magnitude of the mean shift value to detect. | |
| The “Lower Reference” value specified for plotted Negative CUSUM line. Negative CUSUM values are accumulated only when the deviation from the target value exceeds specified K value. K value is half the magnitude of the mean shift value to detect. | |
| Decision Parameter. Factor for determining Decision Interval, H. Generally, h is defined as 5, although sometimes 4 is utilized. |
|
| H is the “Decision Interval,” which acts as a control limit. | |
| Optional. Fast Initial Response or “head start” is typically half of H and is treated as the initial CUSUM value when no data exists. |
Figure 1 Table of parameters and statistics necessary to construct the tabular CUSUM chart.
http://www.infinityqs.com/tech-notes/tabular-cumulative-summation-cusum-chart
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