1. A reliability evaluation system for a multi-state flow network that has a source node, a reception node, at least one connection node between the source node and the reception node, and a plurality of paths having a given flow upper limit from the source node, through the connection node, to the reception node, the reliability evaluation system performed using a computer coupled to a database including data relating to the multi-state flow network for reducing reliability calculation time, the reliability evaluation system comprising: a processor defining, by the computer, each of the plurality of paths as a system state vector, each of the system state vectors having at least one grade, each of the grade having at least one element, so as to define all the elements in the j th grade of the i th system state vector as a set, wherein j is i−1; a comparator comparing, by the computer, values of all the elements in the set, excluding the element with a greater value and other related thereof in all grades in the i th system-state vector when only one element in the set except the element with greater values so as to obtain remaining elements, or, when only one element is in the set, letting the element to be the remaining element; and a calculator using a great common factor (GCF) calculating, by the computer, means to calculate initial reliability based on a first system-state vector and a second system-state vector of the plurality of paths, and using the GCF calculating means to perform the calculation of the remaining element to obtain a calculation results, summing the initial reliability and the calculation results so as to obtain a reliability of the multi-state flow network.