A lower bound of reliability calculating method for lattice system with non-homogeneous components

•A general two-dimension lattice system, “k-within-r × s-out-of-m × n” model, with non-homogeneous components is proposed.•A lower bound of system reliability calculating method is developed by employing finite Markov chain imbedding approach.•The system, in which the components are positioned in the cylinder shape, can be translated into the two-dimension lattice model to obtain the system reliability.