Failure mode and effect analysis (FMEA) is a method used to detect causes of failures that may occur in a product or process, and FMEA is more important to prevent a failure before existing by computerized controllers in many industries. The control mechanism must have the ability to calculate and interpret the risk priority number (RPN) value for a fault mode. RPN consists of the ratio values of severity, occurrence, and detectability in FMEA for failure prioritization in order to provide a proper mechanism under this uncertain environment. So, this study is to develop a new grey failure mode and effect analysis (GFMEA) approach by combining grey relational analysis (GRA) with the mass gravity theory (MGT). A new RPN calculation technique based on the mass gravity law has been developed by calculating the relationship between the weights of each process for the production process. The problems resolved within the company without reflection to customers and were detected in the next operations for a steel-door manufacturing process. Hence, the new RPN values are more reliable for decision-makers in the process of production and operations management and obtained with efficient solutions for use to computerized FMEA process.