Optimal allocation of multistate elements in a linear consecutively-connected system

A linear consecutively-connected system consists of N+1 linear ordered positions. M s-independent multistate elements with different characteristics are to be allocated to the first N positions. Each element can provide a connection between the position to which it is allocated and the next few positions. The reliability of the connection for any given element depends on: (1) the position to which it is allocated; and (2) the number of positions it connects. The system fails if the first position (source) is not connected with the N+1 position (sink). An algorithm based on the universal generating function method is suggested for the linear consecutively-connected system reliability determination. This algorithm can handle cases in which any number of multistate elements are allocated in the same position while some positions remain empty. In many cases, such uneven allocation provides greater system reliability than the even one. A genetic algorithm is used as an optimization tool to solve the optimal element-allocation problem.