The probability model is used to analyze the fault tolerance of mesh. To simplify its analysis, it is as-sumed that the failure probability of each node is independent. A 3-D mesh is partitioned into smaller submeshes,and then the probability with which each submesh satisfies the defined condition is computed. If each submesh satis-fies the condition, then the whole mesh is connected. Consequently, the probability that a 3-D mesh is connected iscomputed assuming each node has a failure probability. Mathematical methods are used to derive a relationship be-tween network node failure probability and network connectivity probability. The calculated results show that the 3-D mesh networks can remain connected with very high probability in practice. It is formally proved that when thenetwork node failure probability is boutded by 0.45 %, the 3-D mesh networks of more than three hundred thousandnodes remain connected with probability larger than 99 %. The theoretical results show that the method is a power-ful technique to calculate the lower bound of the connectivity probability of mesh networks.
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