The concept of life cycle sustainability assessment provides an interdisciplinary space to discuss the main challenges in addressing sustainability from a long-term perspective. However, uncertainty related to cost parameters constitutes one of the main challenges in LCC. This uncertainty prevents managers from precisely anticipating the exact values of important variables. These variables include the costs of spare parts inventories, which in some cases can constitute high percentages of the total cost of a product or service. We propose an activity-based costing model that handles uncertainty using triangular numbers, along with a matrix representation, and Weibull functions to incorporate the projected equipment reliability into the model. A case study based on a spare parts distribution center, which serves the mining industry in Northern Chile, is presented. The results obtained are compared with a traditional costing method. The advantage of using the proposed approach over the traditional one is evident. Future research is directed towards the implementation of a larger number of inventory policies, along with experimentation with other types of fuzzy numbers.