The major reasons for low compressive strength tests are:

High air content in the concrete (and test specimens); and
Errors in production and unanticipated factors during delivery.
It is important that procedures are conducted in accordance with ASTM standards. Almost all deficiencies in handling and testing cylinders will result in a lower measured strength. All violations add up to cause significant reductions in measured strength. The more significant factors are: improperly finished surfaces; initial curing over 80°F (27°C); frozen cylinders; extra days in the field; damage during transportation; delay in stripping molds and curing at the lab; improper capping; and insufficient care in breaking cylinders.
The laboratory should be held responsible for deficiencies in its procedures. Field-testing technicians and laboratory personnel should be certified; construction workers untrained in concrete testing must not make and handle cylinders. ACI 318 requires laboratories to conform to ASTM C1077 for their quality system and personnel qualifications. Laboratories should be inspected by the Cement and Concrete Reference Laboratory (CCRL) laboratory inspection or an equivalent program. Field testing personnel must have a current ACI Grade I Field Testing Technician certification or equivalent. Laboratory personnel should have the ACI Grade I and II Laboratory Testing Technician and/or the ACI Strength Testing Certification, or equivalent.
If the deficiency justifies investigation, first verify testing accuracy and then compare the structural requirements with the measured strength. If testing is deficient or if strength is greater than actually needed in that portion of the structure, there is little point in investigating the in-place strength. However, if procedures conform to the standards and the strength as specified is required for the structural capacity of the member in question, further investigation of the in-place concrete may be required (CIP 10).