Recently papers investigating problems on detection of the moment of occurrence of an attack on various systems were published. In particular, they consider "Dos-attacks" or attacks like of "denial of service" in a computing system and subsequent changes of the protocol of processing of input assignments. These studies are actual now. The main difference between the paper and previous works is in selection of another formula for setting the probability of a system destruction as a result of the attack. Another major difference from previous work is the use of beta distribution instead a truncated normal distribution for specifying distribution of a random moment of occurrence of attacks.