Maintenance expenditures contribute to a considerable part of the cost in industrial companies. Accordingly, Failure Mode Effects and Criticality Analysis (FMECA) is used to rationalize the efforts and expenditures dedicated to the maintenance of engineering systems by ranking different industrial systems’ components regarding their criticality to keep them operating reliably. In this study, additional operational parameters were considered to improve the FMECA-derived maintenance schedule, which is anticipated to result in a large reduction in maintenance costs, since the majority of the examined articles discussed their investigations using the commonly used FMECA. As a case study, two main machines of a spinning factory are selected. FMECA application entails possible failure modes analysis of each component. Relative failure mode frequency and severities are obtained from consulting experienced engineers’ and managers’ opinions. Accordingly, the corresponding criticality index is calculated. Risk Priority Number (RPN) is employed to rank different machine components regarding their criticalities and a Relative Risk Priority Number (RRPN) is proposed to decide their most appropriate maintenance policy after considering the operational parameters.