Many enterprises consider several criteria during data transmission such as availability, delay, loss, and out-of-order packets from the service level agreements (SLAs) point of view. Hence internet service providers and customers are gradually focusing on tolerable error rate in transmission process. The internet service provider should provide the specific demand and keep a certain transmission error rate by their SLAs to each customer. This paper is mainly to evaluate the system reliability that the demand can be fulfilled under the tolerable error rate at all sinks by addressing a stochastic node-failure network (SNFN), in which each component (edge or node) has several capacities and a transmission error rate. An efficient algorithm is first proposed to generate all lower boundary points, the minimal capacity vectors satisfying demand and tolerable error rate for all sinks. Then the system reliability can be computed in terms of such points by applying recursive sum of disjoint products. A benchmark network and a practical network in the United States are demonstrated to illustrate the utility of the proposed algorithm. The computational complexity of the proposed algorithm is also analyzed.