Computing Submesh Reliability in Two-Dimensional Meshes

An analytical model for computing submesh reliability is proposed in this paper. The system is considered operational as long as a functional submesh of the required size is available. We use the principle of inclusion and exclusion to find the exact probability of having a functional submesh within a partition of the mesh. The reliability of a partition is then used to approximate the submesh reliability of the system and thus this model is called partitioned mesh (PM) model. The partitions are taken along either dimension of the mesh. The selection of the dimension on which the partitions are made is based on the required submesh size. It is shown that the submesh reliability in every partition reduces to a polynomial with only two terms. The partitioned mesh model is validated with simulation and compared with the earlier proposed approximation techniques. It is shown that the PM model provides better approximations for submesh reliability with constant computational complexity.