          What is it: A cumulative sum (CUSUM) chart plots the cumulative sums of the deviations of each sample value from the target value. The CUSUM control chart is good at detecting small shifts away from the target with only minimal data. A CUSUM Chart is a control chart for variables data which plots the cumulative sum of the deviations from a target. A cusum chart is a type of control chart (cumulative sum control chart). It is used to detect small changes between 0-0.5 sigma. For larger shifts (0.5-2.5), Shewart-type charts are just as good and easier to use. CUSUM charts plot the cumulative sum of the deviations between each data point (a sample average) and a reference value, T. Unlike other control charts, one studying a cusum chart will be concerned with the slope of the plotted line, not just the distance between plotted points and the centerline. Critical limits for a cusum chart are not fixed or parallel. And a mask in the shape of a V is usually laid over the chart with the origin over the last plotted point. Previous points covered by the mask indicate the process has shifted.

Why use it: The advantage of CUSUM is that each plotted point includes several observations, so you can use the central limit theorem to say that the average of the points (or the moving average in this case) is normally distributed and the control limits are clearly defined. As with other control charts, CUSUM charts are used to monitor processes over time. The charts' x-axes are time based, so that the charts show a history of the process. For this reason, you must have data that is time-ordered; that is, entered in the sequence from which it was generated. If this is not the case, then trends or shifts in the process may not be detected, but instead attributed to random (common cause) variation.

Where to use it: Any process where small shifts in the process mean faster than conventional control charts.

When to use it: When to Use a CUSUM Chart CUSUM (or Cumulative Sum) Charts are generally used for detecting small shifts in the process mean. They will detect shifts of .5 sigma to 2 sigma in about half the time of Shewhart charts with the same sample size (Montgomery 1991). The point at which shifts occur is easy to detect by an inflection in the plotted points. They are, however, slower in detecting large shift in the process mean. In addition, typical run tests cannot be used because of the dependence of data points. CUSUM Charts may also be preferred when the subgroups are of size n=1. In this case, an alternative chart might be the Individual X Chart, in which case you would need to estimate the distribution of the process in order to define its expected boundaries with control limits.

How to use it: Cumulative Sum (CUSUM) charts: the ordinate of each plotted point represents the algebraic sum of the previous ordinate and the most recent deviations from the target. A V-mask is used as control limits. Because each plotted point on the CUSUM Chart uses information from all prior samples, it detects much smaller process shifts than a normal control chart would. CUSUM Charts are especially effective with a subgroup size of one. Interpreting a CUSUM Chart A V-mask is used to determine whether the process mean has drifted from the target. Subgroups with missing data are not included in the analysis (i.e. the subgroup sample size, n, must be constant for all subgroups). The performance of the control chart is influenced by the design of the V-mask, which are used to define the CUSUM control limits . The design parameters of the V-mask are the angle (q), which sets the size of the V, and the distance (d), which sets the location of the vertex of the V from the current subgroup. The user influences the value of these parameters by specifying: An interesting property of the CUSUM's V-mask is its ability to detect when a shift occurred. With any control chart, if you are collecting and analyzing data and a process shift occurs, it may be several groups before the shift is detected as a group out of control. The CUSUM chart's V-mask will tend to indicate when the out of control condition originated. For example, if the shift really begins at group 40, the first out of control condition may occur when group 45 is collected, but the CUSUM chart may indicate at that time that group 40 is out of control.

Important information: Must be used in conjunction with some type of X bar and R control chart as the CUSUM chart does not track variation in the range.

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