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. This paper proposes a new theoretical framework, based on Dempster-Shafer Theory (DST), to accommodate this vagueness, and shows how imprecision can give rise to false negative and false-positive inferences. In the artificial intelligence community, two competing methodologies have been proposed to quantify the imprecision inherent with many engineering systems: Fuzzy Set Theory and DST. The former has a strong set-theoretical foundation, while the latter is couched in probability theory. DST assigns upper and lower bounds for the probability on elements of the state space. The paper focuses upon two consequences of vagueness: 1. The influence of imprecise or fuzzy input data on the parameters of the model to be observed. 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 3-valued logic derived from DST "probability" assignments. False-negative and false-positive signals are illustrated by incorporating this information in an additional parameter coupled, with a Boolean AND gate, to each rule of the fault tree. After illustrating the computational simplicity of incorporating DST "probability" assignments, the paper concludes with a discussion of DST advantages for reliability analyses.