Boeing has begun building the first Next-Generation 737 at the program’s new production rate of 35 airplanes a month from 31.5, the company announced on Tuesday evening.

Employees loaded chords and webs manufactured by the Boeing Fabrication division into the company’s newest automated spar assembly tool, the first visible step in the final assembly of the airplane. They then joined the parts to make a spar, the main support structure for the wings.

“The start of spar assembly today demonstrates the progress the 737 team has made,” said Beverly Wyse, vice president and general manager of the 737 program. “This is part of the series of rate increases to meet customer demand for the most popular airplane in aviation history.”

Boeing has taken what it calls a three-fold approach to prepare for the rate increases on the 737 program. The company expects to make production processes more efficient by working with employee process improvement teams, increasing the production capacity with capital investments (such as a new wings system installation line in the Renton factory) and making the site footprint more efficient by moving some production areas, expanding others and decommissioning outdated equipment.

The automated spar assembly tool used to build the first spar is the ninth such machine at the Renton factory, drilling about 1,700 holes and inserting fasteners to make the spar. The tool increases Renton’s wing-building capacity, said Boeing.

Plans call for the 737 production rate to jump to 38 airplanes a month in the second quarter of 2013 and to 42 airplanes a month in the first half of 2014.

Boeing Commercial Airplanes CEO Jim Albaugh has said that the company continues studies into whether the 737 supply chain can accommodate a monthly rate higher than 42. Preparing to introduce the new 737 MAX to the market by 2017, Boeing has yet to decide whether to move production for that airplane to a site other than Renton, Wash., potentially creating more capacity for still further rate hikes. Albaugh has expressed a desire to “aggressively” act to reduce the 737 backlog to less than seven years worth of production, but much depends on the ability of the supply chain to keep pace.