Optimal multilevel protection in series–parallel systems

This paper considers vulnerable systems that can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a performance rate, which is the quantitative measure of a systemʹs ability to perform its task. Both the impact of external factors (attack) and internal causes (failures) affect system survivability, which is determined as the probability of meeting a given demand. In order to increase the systemʹs survivability a multilevel protection is applied to its subsystems. This means that a subsystem and its inner level of protection are in their turn protected by the protection of an outer level. This double-protected subsystem has its outer protection and so forth. In such systems, the protected subsystems can be destroyed only if all of the levels of their protection are destroyed. Each level of protection can be destroyed only if all of the outer levels of protection are destroyed. In such systems, different protections play different roles in providing for the systemʹs survivability. Subject to budget limitations a question arises which protections should be applied to obtain the desired survivability. An algorithm for solving the protection cost minimization problem subject to survivability constraint is presented in the paper. The algorithm is based on a universal generating function technique used for system survivability evaluation and on a genetic algorithm used as an optimization engine. Illustrative example is presented.