This paper proposes an integrated approach to identify, evaluate and improve the potential failures in a service setting. This integrated approach combines Fuzzy cost-based service-specific FMEA (FCS-FMEA), Grey Relational Analysis (GRA) and profitability theory for better prioritization of the service failures by considering cost as an important issue and using the profitability theory in a way that the corrective actions costs are taken into account. Considering profitability with FCS-FMEA and GRA reduces the losses caused by failure occurrence. Besides, a maximization linear mathematical problem is used to select the best mix of failures to be repaired. We apply our approach to an academic example concerning the potential failures diagnosis of the Internal Medicine service of a hospital located in Seoul, Korea. We applied our approach and solved the associated maximization problem by a commercial solver, producing an optimal solution which indicates the most convenient mix of failures to be repaired by considering available budget.