Figure 1.
Schematic representation of the on-line process of detection of outbreak signals and correction of the observed counts series in case of alarm, in order to continually store an outbreak-free baseline.
Table 1.
Detection limits for each of the three algorithms implemented and corresponding alarm scores.
Figure 2.
Automated correction in the BLV series for 2010 in order to remove possible outbreak-signals and excessive noise.
Before attempting to use control charts the data have been pre-processed to remove temporal effects using weekly differencing. The original data are represented in green lines. The series subjected to monitoring are shown in red, superimposed on by blue lines showing the corrected series. Alarms are shown as red triangles along the bottom of each graph.
Figure 3.
Outbreak-signal detection using three algorithms (Shewhart control charts, EWMA control charts and Holt-Winters exponential smoothing) combined using the scoring system and applied to real data.
The top panel plots the Mastitis series for the year 2010. Detection scores for each algorithm are shown as vertical bars, stacked to give a final alarm score which scale is shown in the secondary axis. The gray rectangle is used to mark the limit in the secondary axis which corresponds to the reporting threshold – here 7. The bottom panel shows a similar graph for the BLV series.
Figure 4.
Sensitivity of detection and false alarm rates when the combined algorithms are applied to the simulated mastitis series, with five different shapes of simulated outbreak signals.
The table rows and graph nodes show different final alarm scores used as the reporting threshold. Values in the table correspond to the median among 3 different outbreak magnitudes (1 to 4 times the background activity of the series) and 3 different outbreak lengths (1, 2 and 3 weeks; except for the spike, which is always one single day).
Figure 5.
Sensitivity of detection and false alarms rate in the BLV series.
Panel A shows the sensitivity of detection compared to false alarms rate when all three algorithms combined using the scoring system are applied to the simulated BLV series, with five different shapes of simulated outbreaks injected. The graph nodes show different final alarm scores used as the reporting threshold. Points represent the median among 3 different outbreak magnitudes (1 to 4 times the background activity of the series) and 3 different outbreak lengths (1, 2 and 3 weeks; except for the spike, which is always one single day). The remaining panels show sensitivity and false alarm when each detection algorithm is applied individually, as previously documented in [13].
Figure 6.
Example page of a daily report sent to analysts in case of alarm.
The top table shows the detection score for the three algorithms used, in the last 5 days. Next the data of the last 26 weeks are plotted against the detection score for all three detection algorithms used, stacked to give a final alarm score. The main y-axis is the scale for the data, and the secondary y-axis gives the scale for the detection scores. The gray rectangle shows the range of final alarm score which will not generate an alarm. The bottom panel shows the observed data, superimposed by the data after outbreak-signal removal by the detection algorithm.