A novel approach for failure modes and effects analysis based on polychromatic sets

Traditional failure modes and effects analysis (FMEA) methods lack sufficient semantics and structure to provide full traceability between the failure modes and the effects of the complex system. To overcome this limitation, this paper proposes a formal failure knowledge representation model combined with the structural decomposition of the complex system. The model defines the failure modes as the inherent properties of the physical entities at different hierarchical levels, and employs the individual color, unified color, and Boolean matrix of the polychromatic sets to represent the failure modes in terms of their interrelationships and their relations to the physical system. This method is a structure-based modeling technique that provides a simple, yet comprehensive framework to organize the failure modes and their causes and effects more systematically and completely. Using the iterative search process operated on the reasoning matrices, the end effects on the entire system can be achieved automatically, which allows for the consideration of both the single and multiple failures. An example is embedded in the description of the methodology for better understanding. Because of the powerful mathematical modeling capability of the polychromatic sets, the approach presented in this paper makes significant progress in FMEA formalization.