[Mathematical analysis of the error distributions in flow-systems and consequences for the determination of new...

In connection with the determination of method adapted control limits for the Technicon Autoanalyzer SMA 12/60 (Na+, K+, C1-, Total Protein, Albumin, P, Cholesterol, Urea Nitrogen, Calcium, Creatinine, Bilirubin, Uric Acid) we have investigated the representation of the control variable error distributions by mathematical formulae. The application of orthogonal functions (Gram-Charlier's series type A) proved to be not practicable because of the oscillations occuring at the ends of the distributions. Considerably improved results were obtained by a modified expression of a Gram-Charlier's series of type C, although the tails of the distributions (which are particularly important for the calculation of the fractiles) could not be optimally approximated. However, a very satisfactory approximation of the empirical density functions was obtained when we interpreted the control variables as non-additive superposition of two or three normally distributed quantities with different variances. This enables us to calculate channel specific alarm and control limits, thereby replacing the conventional quality control parameters previously checked and based on the assumption of normal distributions. Thus, an adequate monitoring of the reliability of flow-systems can be achieved.