Optimal allocation of multi-state elements in linear consecutively connected systems with vulnerable nodes

Abstract

A linear multi-state consecutively connected system (LMCCS) consists of N+1 linear ordered positions (nodes). M statistically independent multi-state elements (MEs) with different characteristics are to be allocated at the N first positions. Each element can provide a connection between the position in which it is allocated and the next few positions. The reliability of the connection for any given element depends on the position in which it is allocated and on the number of positions it connects. The system fails if the first position (source) is not connected with ( N+1)th one (sink). Each system node with all the MEs allocated at this node can be destroyed by external impact with a given probability. The system survivability is defined as the probability that at least one path exists from the source to the sink when both external impacts and internal failures can cause MEs unavailability. The algorithm for finding the ME distribution providing the greatest possible LMCCS survivability is suggested. A genetic algorithm is used as the optimization tool. Illustrative examples are presented.