Comparison of quality-control rules used in clinical chemistry laboratories.

Numerous papers have been written to show which combinations of Shewhart-type quality-control charts are optimal for detecting systematic shifts in the mean response of a process, increases in the random error of a process, and linear drift effects in the mean response across the assay batch. One paper by Westgard et al. (Clin Chem 1977;23:1857-67) especially seems to have attracted the attention of users. Here we derive detailed results that enable the characteristics of the various Shewhart-type control schemes, including the multirule scheme (Clin Chem 1981;27:493-501), to be calculated and show that a fundamental formula proposed by Westgard et al. in the earlier paper is in error, although their derived results are not seriously wrong. We also show that, from a practical point of view, a suitably chosen Cusum scheme is near optimal for all the types and combinations of errors discussed, thereby removing the selection problem for the user.