Calculation of a concentration and its random error

In this equation, is the experimental value of y from which the concentration value Xq is to be determined, is the estimated standard deviation of Xg, and the other symbols have their usual meanings. In some cases an analyst may make 

As expected, equation (5.10) reduces to equation (5.9) if m= 1. As always, confidence limits can be calculated as Xq t 2)S, with n - 2) degrees of freedom. Again, a simple computer program will perform all these calculations, but most calculators will not be adequate. 

Using the data from the Section 5.3 example, determine Xq and values and Xq confidence limits for solutions with fluorescence intensities of 2.9, 13.5 and 23.0 units. 

If we wish to improve (i.e. narrow) the confidence limits in this calibration experiment, equations (5.9) and (5.10) show that at least two approaches should be considered. We could increase n, the number of calibration points on the regression line, and/or we could make more than one measurement of yo, using the mean value of m such measurements in the calculation of Xq. The results of such procedures can be assessed by considering the three terms inside the brackets in the two equations. In the example above, the dominant term in all three calculations is the first one -unity. It follows that in this case (and many others) an improvement in precision 

An entirely distinct approach to estimating uses control chart principles (see Chapter 4). We have seen that these charts can be used to monitor the quality of laboratory methods used repeatedly over a period of time, and this chapter has shown that a single calibration line can in principle be used for many individual analyses. It thus seems natural to combine these two ideas, and to use control charts to monitor the performance of a calibration experiment, while at the same time obtaining estimates of The procedure recommended by ISO involves the use of q =2 OT 3) standards or reference materials, which need not be (and perhaps ought not to be) from among those used to set up the calibration graph. These standards 

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