  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.
