The cumulative sum (or Cusum) technique is occasionally offered as an alternative to process behavior charts, even though they have completely different objectives. Process behavior charts characterize whether a process has been operated predictably. Cusums assume that the process is already being operated predictably and look for deviations from the target value. Thus, by replacing process characterization with parameter estimation, Cusums beg the very question process behavior charts were created to address.

To illustrate the Cusum approach and compare it with an average chart, I’ll use the example from page 20 of Shewhart’s first book, Economic Control of Quality of Manufactured Product (Martino Fine books, 2015 reprint).These data consist of 204 measurements of electrical resistivity for an insulator. Shewhart organized them into 51 subgroups of size four, based upon the time order in which the measurements were obtained. Figure 1 gives the averages and ranges for these 51 subgroups.

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