Mean and Variance Rules are More Powerful or Selective than Quality Control Rules Based on Individual Values

Summary: Quality control rules based on individual values are compared with mean and variance rules using theoretical computations and simulations. Simple (13,) and combined individual value rules, e. g. a ls.r/22,/4,,/6* rule, are all less powerful for detection of shifts of location than a mean rule, given identical type I errors. The mean rule is also more robust towards non-normality of data distributions. In most cases, the variance rule has more power towards increased scatter than individual value rules, and it always has the highest selectivity. Thus, the simple computations that are required for derivation of the mean and variance result in increased power or selectivity. In particular, in the computerization of quality control, the traditional mean and variance rules are preferable to more or less complicated "multi-rules " proposed for computerized quality control