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Optimal Discrete Adjustments for Short Production Runs

Published online by Cambridge University Press:  27 July 2009

Scott A. Vander Wiel
Scott A. Vander Wiel
Affiliation:
AT&T Bell Laboratories, Murray Hill, New Jersey 07974
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Abstract

Diameter measurements on successive metal hubs from a machining operation are modeled using a random walk with observation error and linear drift corresponding to tool wear. After producing and measuring a hub, the depth of the cutting tool on the lathe can be adjusted in integer multiples of 0.0001 inches. How should the tool be adjusted?

An optimal discrete adjustment strategy is derived assuming that the lathe automatically corrects for deterministic tool wear. The objective is to minimize expected run costs proportional to the sum of squared diameter deviations from a target plus fixed charges for manual tool adjustments. The optimal strategy makes no manual adjustment if an estimate of the process mean is near target. Otherwise, an adjustment is made to return the estimated mean as near to target as possible within the adjustment resolution.

The region where no adjustments are made widens near the end of the production run where adjustments have only short-term impact. The region converges as the number of remaining periods increases. Plots of expected run costs show that the extra cost of discreteness is small at high resolution but is substantial when the adjustment grid is coarse.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 1 , January 1996 , pp. 119 - 151
Copyright
Copyright © Cambridge University Press 1996

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