Graph Theory Concepts in Frequency and Availability Analysis

Steady-state availability and failure frequency are two key indices in a repairable system. They are generally evaluated from Markov models with constant transition rates. Numerical solutions can be found for relatively large systems using computer programs. It is more difficult to obtain general equations for a specific system using transition rate symbols. The determination of these equations usually involves linear simultaneous equations, either directly or using Cramer´s Rule. This paper describes a general purpose graphical approach for obtaining steady-state availability and frequency expressions from a flow graph based on the Markov model. A set of generalised formulae is developed and applied to several configurations. This technique avoids the need to use matrices for developing general purpose equations. Its direct approach is useful to practising engineers and students of reliability concepts.