ABSTRACT
One of the exciting features of belief function models is that they unify the treatment of interval (upper and lower bounds) and data-available models. As the fault tree gates can also be modelled with belief functions (over logical sets) the entire fault tree can be expressed in the language of belief functions. Using a vague belief function in the place of a vacuous belief function does not substantially affect the credibility of the model, but it avoids putting positive plausibility on infinite values of the parameter. This chapter shows belief functions for Poisson processes given expert opinion in the form of an interval containing the failure rate. As the data are different in the Bernoulli and Poisson processes, each kind of process needs its own belief function model. Dempster develops one of the earliest belief functions models for the unknown parameter of the binomial distribution.
