Approximation method and formulas for average unavailability of systems with latent faults

Abstract

Approximation method and formulas are provided for the average per flight probability of failure for aircraft systems whose components can fail latently. The approximations are given for two and three component redundant systems. The accuracy of the approximate formulas is studied by comparing them to the numerical results from a Markov solver. It shows that the approximation is close to the exact result in ultra-high reliability systems for a large range of failure rates of the components. The formulas are useful in representing event combinations involving latent events in fault trees. They could also be used to estimate the average per flight failure probability of more complex systems by a combination of the rare event approximation and the application of the formulas to the minimal cutsets of the system failure event.