Models for Simple Series and Parallel Systems

This chapter looks at very simple series and parallel systems which helps the readers to understand the nature and magnitude of the problem caused by information dependence. In order to gain experience with belief function models, it describes the predictions they make for simple series and parallel systems. These simple systems show a consistent pattern for the belief function estimates: the lower bounds are slightly lower than the Bayesian estimates under the common noninformative priors, and the upper bounds are slightly higher than the Bayesian estimates under the common noninformative priors. The chapter computes the failure beliefs about a two component parallel system where the components are of the same or different types. It considers only Bernoulli processes models for components, and describes a model for parallel Poisson processes. Maximus is a frequency based system; hence, its results are not directly comparable with either the Bayesian or belief function arguments.