A probabilistic foundation for vagueness and imprecision in fault-tree analysis

Fault tree and reliability analyses frequently must rely on imprecise or vague input data. A theoretical framework, based on Dempster-Shafer theory (DST), that accommodates this vagueness and shows how imprecision can give rise to false-negative and false-positive inferences is proposed. DST assigns upper and lower bounds for the probability on elements of the state space. The author focuses on two consequences of vagueness: (1) the influence of imprecise or fuzzy input data on the parameters of the model to be observed, and (2) the result of sensory-device failures or of leaving out relevant variables that can cause false-negative and false-positive inferences. Imprecise input data are modeled through a three-valued logic derived from DST `probability´ assignments. False-negative and false-positive signals are illustrated by incorporating this information in an additional parameter that is coupled, with a Boolean AND gate, to each rule of the fault tree. The computational simplicity of incorporating DST probability assignments and the advantages of DST for reliability analyses are shown