Equipment selection is a key strategic decision in the design of a material handling system, because an improper one will lead to operational problems and unnecessary investment costs. It involves determining the number and combination of loaders and trucks which will move the material, fulfilling a specified production schedule. Previous works have addressed this problem with deterministic approaches, without considering the inter-dependent availability of trucks and loaders. In order to fill this gap, we developed a stochastic model that combines the selection and equipment replacement problems, subject to a stochastic production rate constraint. This is a new idea that will help decision-makers to decide faster and more reliable. The proposed model optimises the fleet by minimising the total life cycle costs. To solve it, we used a linearisation approach that reduces the computational effort. We tested our approach with a benchmark model, using a mining case study. Results indicate that the solutions ensure with a high probability a determined production target, producing good robust solutions compared to the deterministic counterpart.