Control Charts

Many of the univariate algorithms used in biosurveillance are techniques taken from statistical quality control, which is a field concerned with monitoring the quality of a production process. One of the simplest statistical quality control methods that we can apply to surveillance is the control chart. A control chart sets an upper control limit (UCL) and a lower control limit (LCL) on the time series being monitored. If the daily counts remain between the UCL and the LCL, then the process is said to be in control. However, if the daily counts exceed the UCL or go below the LCL, then the process is said to be out of control. When monitoring health-related activity, we are usually concerned with a high number of counts in data. As a result, we signal an alarm only if the process exceeds the UCL.

In order to determine the control limits, we need to measure the behavior of the process under normal conditions. Suppose that we have N observations X1, X2,..., XN from the background activity of the process being monitored. Assuming that the daily counts in the background activity follow a normal distribution, we can estimate the sample mean £ and standard deviation 6 of the normal from the N observations. The formulas are shown in Eqs. 1 and 2.

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