Critical infrastructures (CIs) are the primary source of technogenic/industrial accidents and disasters. A CI is an integral set of interconnected elements that in some specific contexts are considered as a system of systems (SoS). Such characteristics of CIs as efficacy, durability, availability, resilience, safety and risk, to a large extent depend on the reliability (probability of failure-PoF) of the system. If a complex system can be virtually divided into a set of separate modules (usually it’s possible) and the PoF for each of them could be determined, then, for calculating system reliability the structural block-diagram approach is widely used.
In our research the CI model consists of a potentially dangerous object (PDO) and its protection subsystem. It is assumed that the PDO has only two (workable and failure) states. If the protection set of means fails, the system reliability is reduced. Hence, the protection means are considered as a reserve, which increases the PDO reliability.
The existing matrix method for determining reliability is based on the probabilistic-logic method. Its mathematical essence is to use the algebra-of-logic functions for an analytical description of the conditions of the system's operability and their strict relationship with the probability functions. This method did not receive wide recognition as being quite voluminous and time-consuming even when using matrix algebra.
The developed methodology is based on maximizing CI reliability with fixed funds allocated for its security. CI is a system comprised by a substantial number of relatively independent units connected in series and/or parallel (serial-parallel or parallel-serial systems). The CI reliability increase is due to implementation of a set of means (which, in total cost, do not exceed the value of the allocated funds). To assess the contribution of the set of measures to the CI PoF reduction a matrix method was developed that is based on the reliability matrix and the matrix of interrelations of system elements. Some results of implementation of the described method are presented.