## Abstract

Mean and variance rules for quality control are more powerful than rules based on individual values. An algorithm for applying such rules is described that controls type I errors (false alarms), while allowing for multiple levels of quality control samples, correlation between levels, small numbers of preliminary values, replication of samples and autocorrelation arising from random effects. Based on ANOVA and empirical approximations for small samples, the algorithm maintains a low per-batch probability of type I errors. Three statistics are computed, *z** _{m}*,

*z*

*and*

_{b}*z*

*, which are shown by simulations to be primarily sensitive to a concordant shift in the quality control values, a discordant shift in the values, and an increase in random variability, respectively. Simulations also show that for a Gaussian distribution of analytical errors, the per-batch probability of a type I error is likely to be within the range 0.0045–0.0071 for two to four levels where there are 20–100 preliminary batches and the inter-level correlations are between zero and 0.8. This partial separation of out-of-control alarms into three components provides more assistance with trouble-shooting than do multivariate quality control schemes based on Hotelling's*

_{w}*T*

^{2}, while retaining comparable power.

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