Estimating Probability of Failure of a Complex System Based on Partial Information about Subsystems and Components, with Potential Applications to Aircraft Maintenance

In many real-life applications (e.g., in aircraft maintenance), we need to estimate the probability of failure of a complex system (such as an aircraft as a whole or one of its subsystems). Complex systems are usually built with redundancy allowing them to withstand the failure of a small number of components. In this paper, we assume that we know the structure of the system, and, as a result, for each possible set of failed components, we can tell whether this set will lead to a system failure. In some cases, for each component A, we know the probability P(A) of its failure; in other cases, however, we only know the lower and upper bounds for this probability. Sometimes, we only have expert estimates for these probabilities, estimates that can be described as fuzzy numbers.