  A random sequence having two segments being the homogeneous Markov processes
is registered. Each segment has his own transition probability law and the
length of the segment is unknown and random. The transition probabilities of
each process are known and a priori distribution of the disorder moment is
given. The decision maker aim is to detect the moment of the transition
probabilities change. The detection of the disorder rarely is precise. The
decision maker accepts some deviation in estimation of the disorder moment. In
the considered model the aim is to indicate the change point with fixed,
bounded error with maximal probability. The case with various precision for
over and under estimation of this point is analysed. The case when the disorder
does not appears with positive probability is also included. The results
insignificantly extends range of application, explain the structure of optimal
detector in various circumstances and shows new details of the solution
construction. The motivation for this investigation is the modelling of the
attacks in the node of networks. The objectives is to detect one of the attack
immediately or in very short time before or after it appearance with highest
probability. The problem is reformulated to optimal stopping of the observed
sequences. The detailed analysis of the problem is presented to show the form
of optimal decision function.
