Physical Unclonable Function (PUF) is a hardware security primitive with a desirable feature of low-cost. Based on the space of challenge-response pairs (CRPs), it has two categories:weak PUF and strong PUF. Though designing a reliable and secure lightweight strong PUF is challenging, there is continuing efforts to fulfill this gap due to wide range of applications enabled by strong PUF. It was prospected that the combination of MAX and MIN bit-wise operation is promising for improving the modeling resilience when MAX and MIN are employed in the PUF recomposition. The main rationale lies on the fact that each bit-wise might be mainly vulnerable to one specific type of modeling attack, combining them can have an improved holistic resilience. This work is to first evaluate the main PUF performance, in particular,uniformity and reliability of the OR-AND-XOR-PUF(OAX-PUF)-(x, y, z)-OAX-PUF. Compared with the most used l-XOR-PUF, the (x, y, z)-OAX-PUF eventually exhibits better reliability given l=x+y+z without degrading the uniformity retaining to be 50%. We further examine the modeling resilience of the (x, y, z)-OAX-PUF with four powerful attacking strategies to date, which are Logistic Regression (LR) attack, reliability assisted CMA-ES attack, multilayer perceptron (MLP) attack, and the most recent hybrid LR-reliability attack. In comparison with the XOR-APUF, the OAX-APUF successfully defeats the CAM-ES attack. However, it shows no notable modeling accuracy drop against other three attacks, though the attacking times have been greatly prolonged to LR and hybrid LR-reliability attacks. Overall, the OAX recomposition could be an alternative lightweight recomposition method compared to XOR towards constructing strong PUFs if the underlying PUF, e.g., FF-APUF, has exhibited improved resilience to modeling attack, because the OAX incurs smaller reliability degradation compared to XOR.