Rare events pose a problem is an observed chain of radioactive decays that
of the background, or are they genetically linked? The paper suggests an ap
proach for the problem solution, based on formalization of the background c
oncept. This approach is an inevitable alternative to other methods, which
require the a priori information about the linked decays, in a situation wh
en such information is absent, but, instead, the background information is
available, e.g., from the calibration measurements. The method is illustrat
ed by the analysis of data registered in the experiment on the synthesis of
the element 114 as one of practically important examples of the analysis o
f rare events.