The aim of this study was to find an analytic solution to the problem of determining the optimal capacity of a batch-storage network to meet the demand for finished products in a system undergoing random failures of operating time and/or batch material. The superstructure of the plant considered here consists of a network of serially and/or parallel interlinked batch processes and storage units. The production processes transform a set of feedstock materials into another set of products with constant conversion factors. The final product demand flow is susceptible not only to short-term random variations in the cycle time and batch size but also to long-term variations in the average trend. Some of the production processes have random variations in product quantity. The spoiled materials are treated through regeneration or waste disposal processes. All other processes have random variations only in the cycle time. The objective function of the optimization is minimizing the total cost, which is composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units. A novel production and inventory analysis, the PSW (periodic square wave) model, provides a judicious graphical method to find the upper and lower bounds of random flows. The advantage of this model is that it provides a set of simple analytic solutions while also maintaining a realistic description of the random material flows between processes and storage units; as a consequence of these analytic solutions, the computation burden is substantially reduced. The proposed method has the potential to rapidly provide very useful data on which to base investment decisions during the early plant design stage. It should be of particular use when these decisions must be made in a highly uncertain business environment. (c) 2006 American Institute of Chemical Engineers.