We consider a classic adjustment method, introduced by Frank Grubbs, t
o which we refer as the harmonic adjustment rule. Grubbs gave a constr
uctive proof of continuous optimality, that is, the rule minimizes the
expected quadratic loss (EQL) every step of the way. We introduce a g
eneralized procedure that allows skipping some adjustments without los
ing information. We also show how to optimize the sample size. Finally
, we show that the harmonic rule is especially advantageous when adjus
tments can be biased, but that there is a limit to its usefulness when
the sample size is large and adjustments are subject to random error.
In the latter case, skipping smalt adjustments becomes particularly a
ttractive.