Comparison of control charts for monitoring clinical performance using binary data.

BACKGROUND: Time series charts are increasingly used by clinical teams to monitor their performance, but statistical control charts are not widely used, partly due to uncertainty about which chart to use. Although there is a large literature on methods, there are few systematic comparisons of charts for detecting changes in rates of binary clinical performance data. METHODS: We compared four control charts for binary data: the Shewhart p-chart; the exponentially weighted moving average (EWMA) chart; the cumulative sum (CUSUM) chart; and the g-chart. Charts were set up to have the same long-term false signal rate. Chart performance was then judged according to the expected number of patients treated until a change in rate was detected. RESULTS: For large absolute increases in rates (>10%), the Shewhart p-chart and EWMA both had good performance, although not quite as good as the CUSUM. For small absolute increases (<10%), the CUSUM detected changes more rapidly. The g-chart is designed to efficiently detect decreases in low event rates, but it again had less good performance than the CUSUM. IMPLICATIONS: The Shewhart p-chart is the simplest chart to implement and interpret, and performs well for detecting large changes, which may be useful for monitoring processes of care. The g-chart is a useful complement for determining the success of initiatives to reduce low-event rates (eg, adverse events). The CUSUM may be particularly useful for faster detection of problems with patient safety leading to increases in adverse event rates.  

Choosing parameter values for a geometric CUSUM chart for detecting an upward shift in a proportion

This article considers the task of providing practical advice to quality engineers and practitioners on the choice of values for the two parameters of a geometric CUSUM control chart. This CUSUM chart was developed to enable the detection of sudden shifts from an acceptable level for a proportion (p) such as fraction nonconforming. In the first part of the article, tables are presented listing recommended parameter-choices for each of 18 in-control levels for p in the range (0.04 to 0.001) for detection of each of five sizes of upward shift. In the second part of the article, some empirical relationships among the parameter values are identified. These relationships are used with interpolation to design geometric CUSUM schemes for any in-control level (pa) of p within the range covered by the tables, and with extrapolation for levels of pa as low as 0.0001. Because of the equivalence between a geometric CUSUM and a Bernoulli CUSUM, the tables and the proposed methods of interpolation and extrapolation also provide assistance in the design of a Bernoulli CUSUM chart

Detecting a downward shift in a proportion using a geometric CUSUM chart

In monitoring an ordered stream of discrete items from a repetitive process, the geometric CUSUM chart may be used to detect sudden shifts from an acceptable level for a process-proportion (p) such as fraction nonconforming. Much of the investigative effort for this CUSUM scheme has been concentrated on the detection of upward shifts, and a recent paper has provided guidance to quality engineers in choosing the parameters (k, h) of such a scheme. In this article, the corresponding task of aiding the choice of parameters for detecting a downward shift is addressed. It is shown, using extensive numerical investigations, that the use of a value for the parameter k based on the Sequential Probability Ratio is not optimal when one is using steady-state evaluation of the detection performance of the CUSUM scheme. Tables are presented listing recommended values of parameters for detection of five sizes of downward shift, for each of 27 in-control levels for p in the range 0.20 to 0.001. Interpolation and extrapolation to find parameter values for other in-control levels of p are also considered, and a range of examples presented. There is an equivalence between a geometric CUSUM scheme and a Bernoulli CUSUM scheme, so that the results of this investigation may also be used in choosing parameter values for a Bernoulli CUSUM chart