Thermal cracking has been a severe issue in asphalt pavements in the cold regions. In the past years, a number of studies have been done using materials testing and statistical methods to give ways for quality control and quality assurance (QC/QA) in asphalt construction. However, these volumetric measurements (density, air voids, thickness, etc.) obtained from materials testing cannot accurately reflect actual mechanical information of the asphalt materials such as relaxing thermal stresses; the factor influencing low temperature cracking of asphalt concrete. This paper presents a statistical approach associated with viscoelasticity using the Bending Beam Rheometer (BBR) to evaluate the construction quality of the asphalt mixtures at low temperatures. An asphalt paving project in Utah was used in the research. Asphalt samples collected from the job sites were shipped back to the laboratory where specimens were tested using the BBR. Creep compliance from the BBR tests were used to perform viscoelastic modeling, and subsequently, the relaxation modulus was integrated to create a band of a confidence interval with the upper limit (UL) and the lower limit (LL). Based on the statistical principle, if any relaxation modulus curve from the field fell out of the range formed by the UL and LL, the construction quality could be considered as a dispute and needs further investigation. If the relaxation modulus curve from the field is located within the band, then it means that the quality of the mixtures meets the requirement. This approach gives a comprehensive review of the construction quality in asphalt pavements at low temperatures.