Strong physical unclonable functions (PUFs) provide a cost-effective authentication solution for resource-limited devices. However, they are susceptible to machine learning (ML) attacks. The lightweight defenses against ML rely on adding non-linearity in the PUF behavior (as the XOR-PUF), or limiting the number of challenges at protocol level (as the lockdown protocol) to constrain learning. Another low-cost approach is to use a non-linear quantization of the response when the PUF provides an integer response, like the RO-PUF. This paper studies the non-monotonic quantization (NMQ) which greatly enhances the security when a large number of quantization level is used. Unfortunately, this makes the PUF highly unreliable, rendering it impractical for authentication purposes. In this study, we propose a solution which circumvents the intrinsic PUF unreliability of NMQ to build an effective authentication protocol. It relies on the Neyman-Pearson test which transforms the native dependability of responses into an asset to get a reliable authentication protocol. To validate this approach, we evaluate our solution in FPGA using a loop PUF (ring oscillator-based PUF) which is a multi-bin PUF. The results show that an authentication success of nearly 100% can be obtained with a high resistance as up to 60% accuracy against three types of ML attacks.