On January 26, 2014, at 1717 central standard time, a Cessna 172K, N4VN, experienced a total loss of engine power when the pilot applied carburetor heat during a visual approach to Quad City International Airport (MLI), Moline, Illinois. The pilot performed a forced landing to a field near Milan, Illinois. The airplane sustained substantial damage to the right wing. The commercial pilot and passenger were uninjured. Visual meteorological conditions prevailed at the time of the accident. The 14 CFR Part 91 personal flight was not operating on a flight plan. The flight originated from Davenport Municipal Airport, Davenport, Iowa, at 1615 and was destined to MLI. The pilot stated that he applied carburetor heat after the MLI air traffic control tower issued a landing clearance for runway 31 after receiving a special visual flight rules clearance to the airport. When he applied carburetor heat about one mile from the runway, the engine quit. He performed a forced landing to a field and touched down at 10-15 mph. The Federal Aviation Administration (FAA) Dupage Flight Standard District Office, West Chicago, Illinois, did not send an FAA maintenance inspector to examine the airplane on-scene following the accident. The National Transportation Safety Board Investigator-In-Charge (IIC) then requested that the airplane owner provide the carburetor and maintenance logbook copies for examination, which were provided by the owner. The airplane owner stated the mechanic who had performed that last annual inspection also installed the carburetor and then removed it for the post-accident examination. The airplane owner stated that during the post-accident removal of the carburetor, there were no mechanical anomalies with the carburetor heat system. The pilot stated that there was an engine rpm decrease when he checked the operation of carburetor heat during an engine run-up prior to departing on the accident flight. The MLI Automated Surface Observing System (ASOS) recorded the following observation: At 1715; special (unscheduled) report; wind – 340 degrees at 11 knots, gust - 21 knots; visibility – 1 statute mile; runway 9 runway visual range – 6,000 feet; weather phenomena - light frozen precipitation; sky condition - broken at 2,700 feet mean sea level, broken at 4,000 feet, overcast at 4,900 feet; temperature - -1 degree Celsius; dew point - -5 degrees Celsius; altimeter – 29.55 inches of mercury. The pilot stated that the airplane did not enter any of the snow showers that were approaching MLI during the accident flight. He said that the snow showers arrived at MLI about 30 minutes after the accident. Special Airworthiness Bulletin, CE-09-35, Carburetor Icing Prevention, includes a graph that shows the probability of carburetor icing for various temperature and relative humidity conditions. At a temperature and dew point as recorded by the MLI ASOS, there was a probability of icing in glide and cruise power. The received carburetor was a Marvel Schebler MA-4-5, part number 10-3676, serial number MS820601, carburetor. Logbook copies included an Authorized Release Certificate, FAA Form 8130-3, which stated the carburetor was overhauled by Marvel-Schebler Aircraft Carburetors, LLC. The date of FAA Form 8130-3 was July 25, 2013. Copies of logbook entry dated June 25, 2013, at a tachometer time of 4,571 hours, stated that an annual inspection was performed. An entry dated October 21, 2013, at a tachometer time of 4,626 hours, stated that the carburetor was [removed and replaced] with an overhauled carburetor, referencing Form 8130-2. The airplane owner said that the tachometer time at the time of the accident was 4,669 hours. Post-accident disassembly examination of the airplane under the supervision of the IIC and an FAA inspector from Dupage Flight Standard District Office revealed that the fuel screen did not contain contaminant, the idle screw was extended about 2 ½ turns, and the throttle valve and float had clearances from the carburetor body that were within service manual specifications. All of the carburetor retaining hardware was in place and secure.