The Fixed-Energy Response-Function Analysis with Multiple Efficiency (FRAM) software is widely used to analyze the isotopic compositions of plutonium or uranium. The uncertainties reported from FRAM have been studied as a function of the live time for plutonium samples with Pu-239 fractions ranging from 60% to 93%. For plutonium fractions, the specific power and other parameters calculated from FRAM, we have found that the associated uncertainties often converge quickly to some asymptotic value. An asymptotic behavior is present when the counting statistical uncertainty is no longer the dominant contributing factor. Thus, the asymptotic behavior can be used to determine when the measurement can be ended in an automated data acquisition and analysis process. With the process, the acquired interim data are saved and FRAM analysis is initiated in command mode without user intervention. Once the data have been analyzed, the FRAM analysis reports are parsed. The reported uncertainties are compared with results from prior analysis automatically. If the uncertainties are found to approach asymptotic behavior, then the data acquisition can be terminated. For samples with an unknown amount of plutonium or uranium, this method has the advantage in that satisfactory results can be obtained automatically without specifying a preset count time. With a conventional measurement method, the same measurement time is often predefined for all samples. The acquired data are analyzed and the results are reviewed manually. If the results are not satisfactory, the process is repeated. For small numbers of measurements, this manual process might be fine. However, to deal with a large number of measurements, it is inefficient. Thus, the proposed automated analysis process would be beneficial to obtain satisfactory results with greatly improved efficiency.