The Harmonic Rule for Process Setup Adjustment with Quadratic Loss

Abstract

We consider a classic adjustment method, introduced by Frank Grubbs, to which we refer as the harmonic adjustment rule. Grubbs gave a constructive proof of continuous optimality, that is the rule minimizes the expected quadratic loss (EQL) every step of the way. We introduce a generalized procedure that allows skipping some adjustments without losing information. We also show how to optimize the sample size. Finally, we show that the harmonic rule is especially advantageous when adjustments 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 small adjustments becomes particularly attractive.