Industrial pressure relief valves must function reliably and effectively to protect pressurized systems from excessive pressure conditions. These valves are essential safety devices that act as cushions to protect piping systems, equipment, and vessels from the risks of high pressure, which can cause damage or even explosions. The objectives of this study were to minimize valve failures, decrease the number of rejected valves in the production line, and enhance the overall quality of pressure relief valves. This work introduces an integrated quality improvement methodology known as the hybrid multi-criteria decision-making (MCDM)—failure mode and effects analysis (FMEA) approach. This approach is based on prioritizing crucial factors for any failure modes in the industrial setting. The presented case study demonstrates the application of a hybrid approach for identifying the fundamental causes of industrial pressure relief valve failure modes and malfunctions. This investigation highlights the applicability of FMEA as a methodology for determining causes and executing remedial actions to keep failures from happening again. FMEA helps uncover the underlying causes of industrial pressure relief valve failures, while the integration of the hybrid MCDM methodology enables the application of four integrated MCDM methods to identify crucial factors. The adopted model addresses the shortcomings of the conventional FMEA by accurately analyzing the relationships between the risk factors and by utilizing several MCDM methods to rank failure modes. Following the application of the adopted methodology, it was discovered that the high-risk failure modes for the pressure relief valve included misalignment of wire, normal wear/aging, rejection of machined parts, mismatch of mating parts, and corrosion. Therefore, risk managers should prioritize developing improvement strategies for these five failure modes. Similarly, failures comprising debris, delayed valve opening, internal leakage, premature valve opening, and burr foreign particles were determined as second essential groups for improvement.