Mobile users in cellular networks produce calls, initiate connections and send packets. Such events have a binary outcome — success or failure. The term “failure” is used here in a broad sense: it can take different meanings depending on the type of event, from packet loss or late delivery to call rejection. The Mean Failure Probability (MFP) provides a simple summary indicator of network-wide performance — i.e., a Key Performance Indicator (KPI) — that is an important input for the network operation process. However, the robust estimation of the MFP is not trivial. The most common approach is to take the ratio of the total number of failures to the total number of requests. Such simplistic approach suffers from the presence of heavy-users, and therefore does not work well when the distribution of traffic (i.e., requests) across users is heavy-tailed — a typical case in real networks. This motivates the exploration of more robust methods for MFP estimation. In a previous work [1] we derived a simple but robust sub-optimal estimator, called EPWR, based on the weighted average of individual (per-user) failure probabilities. In this follow-up work we tackle the problem from a different angle and formalize the problem following a Bayesian approach, deriving two variants of non-parametric optimal estimators. We apply these estimators to a real dataset collected from a real 3G network. Our results confirm the goodness of the proposed estimators and show that EPWR, despite its simplicity, yields near-optimum performance.