Given the recent advances in membrane technology for energy efficient separation, most studies mainly focused on the development of materials while the operability issues of structured modules have been ignored. It has been well established that uncertain disturbances are inevitable and should be considered as an inherent feature in the realistic operations. It is assumed in the present work that the immediate effects of randomly-occurred faults of the system can be characterized mathematically by the uncertain parameters. An ill-designed membrane system, when operated under uncertainties, may perform poorly and result in unnecessary energy waste. Therefore, this work investigates the operational flexibility of membrane modules under the influence of random fault-induced disturbances. The recently developed volumetric flexibility index is adopted as a performance measure. The case studies presented in this paper clearly demonstrate that such an index can indeed provide insights for configuring various fault-tolerant membrane modules.