Optimal separation of elements in vulnerable multi-state systems

In this paper we consider vulnerable systems, which can have different states corresponding to different combinations of available elements composing the system. Each state can be characterized by a system performance rate, which is the quantitative measure of a system’s ability to perform its task. Both the impact of external factors (attack) and internal causes (failures) affect system survivability, which is determined as probability of meeting a given demand.One of the ways to enhance system survivability is to separate elements with the same functionality (parallel elements). Since system elements can have different performance rates and different availability, the way in which they are separated strongly affects system survivability. In this paper we formulate the problem of how to separate the elements of series-parallel system in order to achieve a maximal possible level of system survivability by the limited cost.An algorithm based on the universal moment generating function method is suggested for determination of the vulnerable series-parallel multi-state system survivability. A genetic algorithm is used as optimization tool in order to solve the structure optimization problem.