Range chart for a narrow concentration range in the samples
It is possible to control the precision of the results by performing duplicate analysis of the selected control sample. A range quality control chart (Rmean) can be used to monitor the results of the analysis. The Rmean-chart is set up by analyzing a series of 15 to 20 duplicates and calculating the range (absolute value of the difference). The mean range can then be calculated and plotted on the Rmean-chart as shown in the Figure 1. The method proposed by Youden and Steiner [Statistical Manual of the Association of the Official analytical Chemists, Washington DC, 1975] is based in the assumption that 50 % of the ranges should greater than a value corresponding to 0.845 Rmean, only 5 % greater than 2.456 Rmean (95 % limit) and only 1 % greater than 3.27 Rmean (99 % limit).
Figure 1: Typical Rmean-quality control chart
If 5 or more consecutive points are above the 50 % limit then the analysis is moving out of control and corrective action is needed. Occasionally points will lie above the 95 % limit (about 1 in every 20 points) but points falling above the 99 % limit indicate the need for corrective action. If too many zero values occur it is likely that the results have been rounded to a digit not representing the meaningful precision.
The range value on the Rmean-chart can be used to calculate the standard deviation of the analyses by using the equation:
where S is the standard deviation, R are the ranges and N is the number of samples run in duplicate.