In this paper, we present a methodology for the optimisation of off-grid hybrid systems (photovoltaic diesel-battery systems). A stochastic approach is developed by means of Monte Carlo simulation to consider the uncertainties of irradiation and load. The optimisation is economic; that is, we look for a system with a lower net present cost including installation, replacement of the components, operation and maintenance, etc. The most important variable that must be estimated is the batteries lifespan, which depends on the operating conditions (charge/discharge cycles, corrosion, state of charge, etc.). Previous works used classical methods for the estimation of batteries lifespan, which can be too optimistic in many cases, obtaining a net present cost of the system much lower than in reality. In this work, we include an advanced weighted Ah-throughput model for the lead-acid batteries, which is much more realistic. The optimisation methodology presented in this paper is applied in the optimisation of the electrical supply for an off-grid hospital located in Kalonge (Democratic Republic of the Congo). At the moment, the power supply relies on a diesel generator; batteries are used in order to ensure the basic supply of energy when the generator is unavailable (night hours). The optimisation includes the possibility of adding solar photovoltaic (PV) panels to improve the supply of electrical energy. The results show that optimal design could achieve a 28% reduction in the levelised cost of energy and a 54% reduction in the diesel fuel used in the generator, thereby reducing pollution. Furthermore, we discuss possible improvements to the telecommunications of the hospital. (C) 2016 Elsevier Ltd. All rights reserved.