An expression of uncertainty in calibration using stepwise or separate dilution of a stock solution

The traditional method for linear calibration can estimate the confidence intervals of calibration lines from a set of experimental data for a single calibration line. However, the following situations, often encountered in laboratories, are out of reach of the method, since the concentrations of the standard solutions are not independent of each other: (A) a standard solution is diluted from a more concentrated one in a stepwise way (stepwise dilution); (B) every standard solution for a calibration experiment is prepared from a stock solution, but the stock solution is newly prepared for each calibration (separate dilution with the variable concentration of the stock solution). This paper puts forward a theory to calculate the confidence intervals of calibration lines in the above situations. Analyses made up of sample weighing, dilution, HPLC measurement and calibration with the linear least-squares fitting are taken as examples. The proposed theory is numerically compared to the traditional method.