This paper proposes a new model, a combined m-consecutive-k-out-of-n : F & consecutive-k_c-out-of-n : F system, consisting of n components ordered in a line such that the system fails iff there exist at least k_c consecutive failed components, or at least m non-overlapping runs of k consecutive failed components, where k_c < mk. The components are assumed to be i.i.d. An algorithm for system reliability evaluation, along with an illustrative numerical example, is provided based on the analysis of the system using graphical evaluation and review technique (GERT). The algorithm is also evaluated in terms of the order of computational time. This model has applications to various complex systems such as infrared (IR) detecting and signal processing, and bank automatic payment systems.