We report a systematic study on the limit to nuclear lifetime measurements inthe subnanosecond range. The precision measurement for short lifetimes in the sub nanosecond range needs a gamma-ray fast timing coincidence measurement. Using a 22Na coin source, time resolution of LaBr3(Ce) was measured as 0.266 ps and NaI(Tl) was measured as 0.959 ns. We have measured a half-life of the first 5/2+ excited state in 133Cs using six 2” × 2” inches NaI(Tl) detectors and two 1.5” × 1.5” inches LaBr3(Ce)detectors with gamma ray detector array system(HANULBall). A prompt 356 keV gamma-ray from the 1/2+ → 5/2+ transition triggers a two-fold coincidence with a 81 keV gamma-ray from the 5/2+ → 7/2+ transition in 133Cs. The gamma ray detector signals are fed to a 500 MHz flash ADC so that we can digitize the pulse shapes in every 2 ns. The measured mean lifetime were 6.271 ± 0.069 ns, 6.292 ± 0.057 ns and 6.371± 0.070 ns for LaBr3(Ce) - LaBr3(Ce) pair, LaBr3(Ce) - NaI(Tl) pair and NaI(Tl) - NaI(Tl)pair. We also measured half-life of 160 keV state half-life by measuring 437 keV → 160keV → 0 keV gamma decay cascade. The measured mean half-life in 160 keV state was185 ± 8 ps. We have studied systematic uncertainties in measuring time differences between the prompt and slow gamma-ray signals, which include timing variations with crossing times for different fractional pulse heights, and time jitters. We also simulated scintillation processes, light propagation, photoelectron statistics, and data processing using a Geant4 toolkit