Interpretation & Calculations
As with other control charts, Cu Sum charts are used to monitor processes over time. The 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.
Cu Sum (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 (i.e. X-Bar charts and Individual-X 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 test rules cannot be used because of the dependence of data points. When not available, a Moving Average chart such as offered in our SPC software provides similiar benefits.
Cu Sum Charts may also be preferred when the subgroup size is 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. The advantage of Cusum, EWMA and Moving Average chart 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.
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).