How to Hand-Check a Symbolic Reliability Expression

Checking symbolic reliability expressions is very useful for detecting faults in hand derivations and for debugging computer programs. This checking can be achieved in a systematic way, though it may be a formidable task. Three exhaustive tests are given. These tests apply to unreliability and reliability expressions for noncoherent as well as coherent systems, and to cases when both nodes and branches are unreliable, or when the system has a flow constraint. Further properties of reliability expressions derived through various methods are discussed. All the tests and other pertinent results are proved and illustrated by examples.