Generalized expressions of reliability of series-parallel and parallel-series systems using the Transferable Belief Model

Probability theory is well suited to treat uncertainties when their origin comes only from the natural variability of components’ failure (aleatory uncertainty). On the other hand, if the uncertainties are due to incompleteness, imprecision or ignorance of the reliability data (epistemic uncertainty), several theories can be used. Previous studies have shown that the Transferable Belief Model (TBM) which is an interpretation of the Dempster Shafer theory is a well suited framework to treat both types of uncertainties. Nevertheless, past experiences have proven that the computational cost of the TBM based model grows exponentially with the size of the system. To overcome this situation, generalized expressions were defined so as to have a more efficient way to study the systems’ reliability of series-parallel and parallel-series configurations. Through the use of these expressions, there is no need to go by the TBM operations (conjunctive rule, extensions, etc.) to evaluate the overall system’s reliability.