By Ognyan Ivanov
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Different control charts exist: variables control charts when we are interested in a continuous variable or attributes control charts when we are interested in a dichotomous variable; control charts without memory such as the Shewart chart or with memory such as the exponentially weigthed moving average (EWMA) that averages the data in a way that gives less and less weight to data as they are further removed in time, etcPage (1954); Roberts (1959); Shewhart (1931); Wald (1945). But for all, the objective is to display the variation over time of the process under scrutiny.
Colonoscopy perforation rate, mechanisms and outcome: from diagnostic to therapeutic colonoscopy. Endoscopy. 2009 Nov;41(11):941-51.  Bokemeyer B, Bock H, Huppe D, Duffelmeyer M, Rambow A, Tacke W, et al. Screening colonoscopy for colorectal cancer prevention: results from a German online registry on 269000 cases. European journal of gastroenterology & hepatology. 2009 Jun;21(6):6505.  Crispin A, Birkner B, Munte A, Nusko G, Mansmann U. Process quality and incidence of acute complications in a series of more than 230,000 outpatient colonoscopies.
A CUSUM test statistic is then constructed for each hypothesis in a traditional way (see eq. 2). When the process can only deviate on one side, the corresponding hypothesis H01 or H02 only is tested. For instance, when monitoring binary data (success/failure) one is generally interested in testing only whether the failure rate of a trainee does not deviate by more than an acceptable amount above adequate performance. In that situation, the hypothesis H02 is ignored. This situation can be regarded as akin to non-inferiority trials.