Fault propagation analysis is an important step in determining system reliability and defining fault tolerance strategies. Typically, in the early software design phases, the propagation probability for a fault is assumed to be one. However, the assumption that faults will always propagate highly underestimates reliability, and valuable resources may be wasted on fixing faults that may never propagate. To determine the fault propagation probability, a concept of flat parts is introduced. A flat part is a property of a function; when multiple functions containing flat parts interact with each other, these flat parts undergo a transformation. During this transformation, the flat parts may be killed, preserved, or new flat parts may be generated. Interval arithmetic-based rules to determine such flat part transformations are introduced. A flat part-based propagation analysis can be used to determine the reliability of a software system, or software-driven mechanical system expressed functionally. In addition, the information obtained through flat part-based propagation analysis can be used to add sensors within the flat parts to increase the probability of fault detection, thus increasing the robustness of the system under study.
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