THE HARMONIC RULE FOR PROCESS SETUP ADJUSTMENT WITH QUADRATIC LOSS

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.