Defining Changing Histograms

Within QOD the Kolmogorov difference is called a False Alarm Probability, because it represents the degree to which the comparison could be wrong (false) in deciding two histograms are actually different. The level at which Sample histograms are deemed to be changing can be set by the user, but by default is set to report those histograms with a a False Alarm probability less than 1×10^-3 (see Changing Default Analysis Parameters ). This value was judged on the reliability of the reported False Alarm Probability for data taken under normal running circumstances. Also, the number of errors reported at this setting can be investigated by the shift operator during the lifetime of one analysis sample.

Depending on the histograms being compared a simple application of the Kolmogorov shape test may not be enough to discriminate between changing and static histograms. In these instances the Kolmogorov test is applied to each bin. Resulting False Alarm Probabilities (one for each bin) are used to determine changing histograms (using hbook routine hdiffb). The test looks to see that each bin has a probability less than 1×10 ^-4, and contains more than 100 events to avoid errors due to low statistics. This method ensures that large changes in a single bin do not dominate the overall shape comparison and erroneously label the plot as changing. Any other revisions to the above method will be described when discussing the relevant histogram (Chapter on QOD Monitored Histograms   ).

Histograms are also monitored for long term changes through comparison of the Sample and Total plots. By default these changes are significant at the False Alarm Probability of 1 ×10^-4.