Abstract
This chapter deals with the paradigm of handling system reliability analysis in the Boolean domain as a supplement to (rather than a replacement to) analysis in the probability domain. This paradigm is well-established within the academic circles of reliability theory and engineering, albeit virtually unknown outside these circles. The chapter lists and explains arguments in favor of this paradigm for systems described by verbal statements, fault trees, block diagrams, and network graphs. This is followed by a detailed exposition of the pertinent concept of the Real or Probability Transform of a switching (two-valued Boolean) function, and that of a Probability-Ready Expression (PRE). Some of the important rules used in generating a PRE are presented, occasionally along with succinct proofs. These include rules to achieve disjointness (orthogonality) of ORed formulas, and to preserve statistical independence, as much as possible, among ANDed formulas. Recursive relations in the Boolean domain are also discussed, with an application to the four versions of the AR algorithm for evaluating the reliability and unreliability of the k-out-of-n:G and the k-out-of-n:F systems. These four versions of the algorithm are explained in terms of signal flow graphs that are compact, regular, and acyclic, in addition to being isomorphic to the Reduced Ordered Binary Decision Diagram (ROBDD). An appendix explains some important properties of the concept of Boolean quotient, whose expectation in Boolean-based probability is the counterpart of conditional probability in event-based probability.