  Multivariate data sources with components of different information value seem
to appear frequently in practice. Models in which the components change their
homogeneity at different times are of significant importance. The fact whether
any changes are influential for the whole process is determined not only by the
moments of the change, but also depends on which coordinates. This is
particularly important in issues such as reliability analysis of complex
systems and the location of an intruder in surveillance systems. In this paper
we developed a mathematical model for such sources of signals with discrete
time having the Markov property given the times of change. The research also
comprises a multivariate detection of the transition probabilities changes at
certain sensitivity level in the multidimensional process. Additionally, the
observation of the random vector is depicted. Each chosen coordinate forms the
Markov process with different transition probabilities before and after some
unknown moment. The aim of statisticians is to estimate the moments based on
the observation of the process. The Bayesian approach is used with the risk
function depending on measure of chance of a false alarm and some cost of
overestimation. The moment of the system's disorder is determined by the
detection of transition probabilities changes at some coordinates. The overall
modeling of the critical coordinates is based on the simple game.
