Reliability approximation of k-out-of-n pairs: G balanced systems with spatially distributed units

Various industries are finding increasing uses for k-out-of-n pairs: G balanced systems, an example being an unmanned aerial vehicle. The reliability estimation for such systems is difficult to obtain, due to the complexity of the problem: the operation of the systems depends on not only the number of operating pairs but also their spatial configuration. The computation becomes time-consuming when n is large and k is small, since the number of successful events increases significantly. In this article, we develop a Monte Carlo simulation-based reliability approximation for k-out-of-n pairs: G balanced systems for different scenarios. Numerical examples show that the approximation is accurate and computationally efficient.