Optimizing survivability of vulnerable series–parallel 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 systemʹs 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. We formulate the problem of finding structure of series–parallel multi-state system (including choice of system elements, their separation and protection) in order to achieve a desired level of system survivability by the minimal cost. An algorithm based on the universal 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.