The aim of this study was to find an analytic solution to the problem of determining the optimal capacity (lotsize) of a batch-storage network to meet demand for a finished product 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 to short-term random variations in the cycle time and batch size as well as 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 significantly reduced.