Control charts for health care monitoring under overdispersion

Abstract

An attractive way to control attribute data from high quality processes is to wait till r ≥ 1 failures have occurred. The choice of r in such negative binomial charts is dictated by how much the failure rate is supposed to change during Outof-Control. However, these results have been derived for the case of homogeneous data. Especially in health care monitoring, (groups of) patients will often show large heterogeneity. In the present paper we will show how such overdispersion can be taken into account. In practice, typically neither the average failure rate, nor the overdispersion parameter(s), will be known. Hence we shall also derive and analyze the estimated version of the new chart.

A generalized statistical control chart for over‐ or under‐dispersed data

“…Several works (e.g. References1–4), however, express concern over the use of such a structure, recognizing that the underlying equi‐dispersion assumption is limiting. Focusing on data sets that illustrate over‐dispersion, the increased variation results in numerous data values being falsely detected as out‐of‐control when, in fact, such data are false positives.…”

An Overview of Control Charts for High‐quality Processes

“…In the medical field, one needs to pay special attention to events that are rare but are associated with high risk. The TBE charts are particularly suited to this type of application …”

“…The TBE charts are particularly suited to this type of application. [158][159][160][161][162][163][164] We have reviewed 114 articles (cf . Table II) related to the TBE or high-quality concept, and 63% of the reviewed articles deal with discrete or attribute data, while 31% deal with continuous data, and the remaining (6%) with both.…”

Empirical nonparametric control charts for high-quality processes

“…In addition to the failure rate p,a second parameter is used to accommodate the degree of overdispersion. Indeed, as shown in Albers (2009), the results obtained are far better than those using the basic negative binomial approach. However, neither in Albers, Kallenberg and Nurdiati (2004), nor in Albers (2009), it is pretended that the wider model will achieve a perfect fit.…”

“…Indeed, as shown in Albers (2009), the results obtained are far better than those using the basic negative binomial approach. However, neither in Albers, Kallenberg and Nurdiati (2004), nor in Albers (2009), it is pretended that the wider model will achieve a perfect fit. The precise underlying mechanism remains unknown in either case and by using a more flexible model 'only' a better approximation of reality is achieved.…”