This article presents a topological technique for evaluating the performance of a hybrid flow-shop production system. Such a production system is modeled as a hybrid production network; each workstation of the hybrid production network has stochastic capacity levels. This article evaluates the probability of demand satisfaction as a performance indicator for the hybrid production network, in which the network has multiple lines and each workstation has a distinct defect rate. First, a topological transformation is utilized to transform a hybrid flow-shop production system into a network-structured hybrid production network; then, the hybrid production network is decomposed into several routes for flow analysis. Second, two procedures for two models (Model I considers the hybrid production network with parallel lines, Model II with intersectional lines) are designed to generate the minimal required capacity for workstations to satisfy the given demand. The probability of demand satisfaction is subsequently evaluated in terms of the minimal required capacities by applying the recursive sum of disjoint products algorithm.