Quality Criteria for Analytical Results

Analytical methods, particularly those used by accredited laboratories, have to be validated according to official rules and regulations to characterize objectively their reliability in any special field of application (Wegscheider [1996] EURACHEM/WELAC [1993]). Validation has to control the performance characteristics of analytical procedures (see Chap. 7) such as accuracy, precision, sensitivity, selectivity, specificity, robustness, ruggedness, and limit values (e.g., limit of detection, limit of quantitation). 

Within the scope of quality agreements in production, environment, or laboratory, quality is often stipulated to a standard value x0 (target value). For demands regarding quality, this standard value may be an upper limit (e.g. in case of pollution and contamination) or a lower limit (e.g. for active reagents). The statistical situation is the same when a quality criterion has to exceed or fall below a standard value. The problem is illustrated here by the practical situation of manufacturer and customer as shown in Fig. 4.11. 

If an analytical test results in a lower value x, x0, then the customer may reject the product as to be defective. Due to the variation in the results of analyses and their evaluation by means of statistical tests, however, a product of good quality may be rejected or a defective product may be approved according to the facts shown in Table 4.2 (see Sect. 4.3.1). Therefore, manufacturer and customer have to agree upon statistical limits (critical values) which minimize false-negative decisions (errors of the first kind which characterize the manufacturer risk) and false-positive decisions (errors of the second kind which represent the customer risk) as well as test expenditure. In principle, analytical precision and statistical security can be increased almost to an unlimited extent but this would be reflected by high costs for both manufacturers and customers. 

With the aid of consequences resulting from wrong decisions, risks R can be given for the manufacturer M as well as for the customer C  

The relationship between the target value x0 and the distribution of the critical values are illustrated in Fig. 4.11 for manufacturer (M) and customer (C). For x x0 the quality is better than agreed while x x0 indicates poorer quality. 

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