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Bernoulli processes have been monitored using a wide variety of techniques in statistical process control. The data consist of information on successive items classified as conforming (nondefective) or nonconforming (defective). In some cases, the probability of obtaining a nonconforming item is very small; this is known as a high quality process. This area of statistical process control is also applied to health-related monitoring, where the incidence rate of a medical problem such as a congenital malformation is of interest. In these applications, standard Shewhart control charts based on the binomial distribution are no longer useful. In our expository paper, we review the methods implemented for these scenarios and present ideas for future work in this area. We offer advice to practitioners and present a comprehensive literature review for researchers.

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