An Algebra of Fault Tolerance

Every system of any significant size is created by composition from smaller sub-systems or components. It is thus fruitful to analyze the fault-tolerance of a system as a function of its composition. In this paper, two basic types of system composition are described, and an algebra to describe fault tolerance of composed systems is derived. The set of systems forms monoids under the two composition operators, and a semiring when both are concerned. A partial ordering relation between systems is used to compare their fault-tolerance behaviors.