A least-squares fit of exponential functions to a measured radioactive decay rate curve provides an estimate of the half-life and its statistical uncertainty in the assumption that all deviations from the theoretical curve are purely of a random nature. The result may be biased and the error underestimated as soon as the experiment suffers instabilities that exceed the duration of individual measurements. Contrary to long-term systematic errors, medium-frequency cyclic perturbations may be observable as autocorrelated structures in the residuals. In this work, an empirical decomposition algorithm is used to separate medium-frequency effects from the random statistical component in the fit residuals, such that custom error propagation factors can be calculated. A theoretical study of error propagation is made for sine and square wave perturbations. The empirical decomposition method is demonstrated on a synthetic spectrum, a time series of solar neutrino detection rates, and two experimental decay curves of ¹³⁴Cs measured in an ionisation chamber.

指数函数与测量的放射性衰变率曲线的最小二乘拟合提供了半衰期及其统计不确定性的估计，假设所有偏离理论曲线的偏差都是纯随机的。一旦实验遇到超过单个测量持续时间的不稳定性，结果可能有偏差并且误差被低估。与长期系统误差相反，中频循环扰动可以作为残差中的自相关结构被观察到。在这项工作中，使用经验分解算法将中频效应与拟合残差中的随机统计分量分开，以便可以计算自定义误差传播因子。对正弦波和方波扰动的误差传播进行了理论研究。在电离室中测得的¹³⁴ Cs。