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During the control phase of the project, we sometime want to check how the small shift is going to impact the process target. We need to use Cumulative Sum (CUSUM) in these scenarios. It is the sum of deviation of individual sample or subgroup average from the target. These cumulative deviations over time are plotted in the CUSUM control chart and this clearly help us to identify when the process if out of control. As we are aware, the X-bar helps is also a control chart which monitors the average or the mean of the process and how it changes over time. Below are some of the distinct differences between CUSUM Chart and X-Bar Chart: CUSUM Chart X-Bar Chart Monitors the quality of a stable process when the expected shift is small Monitors the movement of average of the process over the time Used when there is high cost of false alarm Used when there is low cost of false alarms Used when there is high cost of repairing a process Used when there is low cost of repairing a process Faster detection of drift in the process with same sample size Takes almost double the time to find the drift with same sample size Subgroup size is generally 1 Subgroup size is generally 5

Advantages of CUSUM chart over Individual, X BAR chart 1. CUSUM chart is used to detect smallest variation from target value. This chart is used where sub grouping is not required / feasible, however, there is a need to detect very small shift (less than 1.5 sigma). The biggest advantage is that the user can determine the degree of shift that needs to be detected This type of chart can also be used where the process average is expected to naturally shift, for e.g. chemical industries 2. This chart is a better choice when the objective is to control the data point to a target value by making necessary process adjustments than plotting an X Bar or Individual chart and then trying to identify special causes for variation Example using data (reference source from Cumulative Sum Chart (CUSUM) - Six Sigma Study Guide) Minitab or other SPC tools can auto calculate the upper and lower CUSUM for all values CUSUM chart shows that the process is deviating from target from sample 13, whereas, the below IMR chart shows that process is in control and is stable. Hence CUSUM chart is more useful to detect small changes in the process mean compared to X Bar and I MR charts

The CUSUM chart is used to detect very small shifts to the process. It is able to detect these small shifts because it incorporates the data from the sequence of the sample. It plots the Cumulative SUMs of the deviations of each value in the sample from the laid down target. These deviations should vary randomly above and below zero. A trend in either way would indicate a shift in the process mean. Being cumulative helps in the detection of very minor drifts to the process mean and will either cause a steady increase or decrease in the cumulative deviation values. The sample values can be individual measurements or the means of the subgroups. In case we do not want to detect very small shifts, variables chart for subgroups such as the Individual-MR Chart or the Xbar-R Chart. In case the data is the count of defects/defectives, the U or P Chart can be used. Example A quality engineer at a plant that assembles automobile engines monitors the movement of crankshafts in the engines. In an operating engine, parts of the crankshaft move up and down a certain distance from the baseline position. The engineer took five measurements per day from September 28 through October 15 and then 10 per day from October 18 through 25. The example of the same data displaying a CUSUM Chart and an Xbar R Chart shows that while the X-Bar R Chart is in control, the CUSUM Chart is able to detect the minor shift in the process mean indicated by the red dots in the control chart. References https://support.minitab.com/en-us/minitab/18/help-and-how-to/quality-and-process-improvement/control-charts/how-to/time-weighted-charts/cusum-chart/before-you-start/overview/ https://support.minitab.com/en-us/minitab/19/help-and-how-to/quality-and-process-improvement/control-charts/how-to/time-weighted-charts/cusum-chart/methods-and-formulas/methods-and-formulas/ Example Data from support.minitab.com https://support.minitab.com/en-us/minitab/19/help-and-how-to/quality-and-process-improvement/control-charts/how-to/time-weighted-charts/cusum-chart/before-you-start/example/