Optimizing resource allocations to improve system reliability via the propagation of statistical moments through fault trees

Fault tree analysis remains a significant alternative for modeling and analyzing reliability and failure modes. Traditionally, the probabilities of the basic events are assumed as point estimates from which the fault tree is used to estimate the probability of the top failure event. This paper instead proposes using this framework for a different purpose: framing the model parameters describing the basic events as random variables, which collectively contribute to the statistics of the estimate of the top failure event. An approach for uncertainty propagation via statistical moments is developed for both static and dynamic gates with specific consideration of the effects of the dependency conditions for different distribution types. Assuming there is a cost to acquire model parameters with reduced uncertainty, this framing can thus be used to identify the best set of model parameters possible within a constrained budget to minimize uncertainty in the resulting estimate of the top failure event. With these models in place, the statistical moments of the top event can be connected to all lower levels, and the statistics in the estimate of the top event can be optimized with a given cost constraint (e.g. allocating resources to reducing uncertainty in the knowledge of basic events to minimize variance in the estimate of the top failure event). This optimization of the uncertainty in the top event is demonstrated with a case study.