From the perspective of network analysis, the manufacturing system can be constructed as a stochastic-flow network, since the capacity of each machine is stochastic (i.e. multistate) owing to the failure, partial failure, and maintenance. Considering reworking action and different failure rates of machines, the input flow (raw materials/work in process) processed by each machine might be defective, and therefore the output flow (work in process/products) would be less than the input amount. To evaluate the capability of the manufacturing system, we measure the probability that the manufacturing network can satisfy demand. Such a probability is defined as the system reliability. A decomposition method is first proposed to divide the manufacturing network into one general processing path and one reworking path. Subsequently, two algorithms are utilised for different network models to generate the lower boundary vector of machine capacity to guarantee that the manufacturing network is able to produce sufficient products fulfilling the demand. The system reliability of the manufacturing network can be derived in terms of such a capacity vector afterwards.

Network structures have been diffusely adopted in logistics systems, where the most critical target is completing the delivery within the promised timeframe. This paper focuses on a single commodity in a multistate intermodal logistics network (MILN) with transit stations and routes to involve three parameters: a route’s capacity, delivery time and time window. There is a carrier along each route whose number of available containers is multistate because the containers can be occupied by other customers. The delivery time consisting of the service time, travel time and waiting time varies with the number of containers and vehicle type. The arrival time at the transit station should be within the time window, the interval between the earliest and latest acceptable arrival times. This paper evaluates the system reliability, the probability that the MILN can successfully deliver sufficient amount of the commodity to meet market demand via several transit stations under the delivery time threshold and time windows. The system reliability can be treated as a delivery performance index and is evaluated with a proposed algorithm in terms of minimal paths. A practical case of scooter parts distribution between Taiwan and China is presented to emphasise the management implications of system reliability.