Belief Function Models for Simple Series and Parallel Systems

Belief functions are a versatile class of mathematical models which include as cases both first order logic and probability statements. Although belief function models have a higher computational cost than probabilistic models, recent progress with graphical belief function models has made complex belief function models computationally feasible. This is especially true in models which have a natural graphical structure such as that provided by fault trees. This paper explores the issues involved in constructing belief function models for risk assessment by producing belief function models for simple problems. In particular, it constructs belief function models for Bernoulli and Poisson processes and extends those models for simple series and parallel systems. Key Concepts: Bayesian Analysis, Bernoulli Process, Binomial Distribution, Poisson Process, Retiabilzty. L A brief review of belief functions The theory of belief function (Shafer[1976J) is a theory of certain upper and lower probability models arising from some work of Dempster[1966, 1968] extending the Bayesian and fiducial arguments. One of the most attractive features of belief functions is that a unified framework can model both probabilistic and statements. The use of a more general belief function model incurs an additional computational cost. Recent hence seems work in graprucar belief function models (Dempster and Kong[1988], Shafer, Shenoy and Me:lloullIHI1:\(:S!. and has made with belief function models feasible. Fault trees nrovide lnrmll'p whether contributions In