The Harmonic Rule for Process Setup Adjustment with Quadratic Loss

Dan Trietsch

31 citations0/0 files storedJournal of Quality Technology

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Advanced Statistical Process Monitoring Management and Optimization Techniques Optimal Experimental Design Methods

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.

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References

1932Economic Control of Quality of Manufactured Product.1986Introduction to Quality Engineering: Designing Quality into Products and Processes 1992Taguchi's Parameter Design: A Panel Discussion 1985What Is Total Quality Control 1983An Optimum Procedure for Setting Machines or Adjusting Processes

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2003Integration of Sequential Process Adjustment and Process Monitoring Techniques 2006Statistical process adjustment: a brief retrospective, current status, and some opportunities for further work 2009A General Harmonic Rule Controller for Run-to-Run Process Control 2004Setup adjustment under unknown process parameters and fixed adjustment cost 2005Setup Error Adjustment: Sensitivity Analysis and a New MCMC Control Rule 2004A Sequential Markov Chain Monte Carlo Approach to Set-up Adjustment of a Process over a Set of Lots 2006Setup Adjustment of Multiple Lots Using a Sequential Monte Carlo Method 2008Economical operation of the C pm control chart for monitoring process capability index

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