The ATLAS Collaboration at the LHC has chosen the resistive Micromegas technology, along with the small-strip Thin Gap Chambers, for the high luminosity upgrade of the first muon station in the high-η region (i.e.1.3 < |η| < 2.7), the so called New Small Wheel project. After the R&D phase, design and prototyping phase, the first series production Micromegas quadruplets are being constructed at the involved construction sites (France, Germany, Italy, Russia and Greece). All the Micromegas boards produced in industries and delivered at CERN are undergoing a detailed quality control and quality assurance under the supervision of the CERN group. This is a big step forward towards the installation of the New Small Wheel foreseen for the LHC long shutdown in 2019 and 2020. The construction of the four types of large size quadruplets, all having trapezoidal shapes with surface areas between 2 and 3 m2, will be briefly described. The achievement of the requirements for these detectors revealed to be even more challenging than expected, when scaling from the small prototypes to the large dimensions. The encountered problems and the proposed solutions are to a large extent common to other micro-pattern gaseous detectors. The final quality on the achieved mechanical precision, and on the high-voltage stability, are described together, with results from test-beam studies with the first production chambers.