Reliability block diagram extensions for non-parametric probabilistic analysis

Multi-Valued Reliability Block Diagrams (MVRBD) are introduced as a generalization of classical reliability block diagrams (RBD) commonly used in system analysis. MVRBD offer the advantage of allowing systems and subsystem components to be modeled with arbitrary hazard failure rate relationships. MVRBD are based upon a multiple-valued discrete switching algebra that is functionally complete with constants thereby affording a corresponding model to be formulated for any system that is capable of being modeled in a reliability block diagram form. The utility of this new model is that system failure and reliability analysis can be performed without restricting component hazard rate relationships to the binary case of either "failure" or "fully operational." The incorporation of any desired number of "degraded" states into the MVRBD model allows for non-parametric probability mass functions (pmf) to be used. Any arbitrary number of intermediate system states of "degraded" may be incorporated into the MVRBD model without significant increase in the complexity of the analyses methodologies.