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Optimal discrete adjustments for short production runs. (English) Zbl 1093.90528
Summary: 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 meakes 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 substantially when the adjustment grid is coarse.

MSC:
90B30 Production models
62N99 Survival analysis and censored data
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[1] DOI: 10.2307/1269952 · Zbl 0806.62083 · doi:10.2307/1269952
[2] DOI: 10.2307/1270028 · doi:10.2307/1270028
[3] Box, Bulletin of the International Statistical Institute 34 pp 943– (1963)
[4] Bather, Journal of the Royal Statistical Society, Series B 25 pp 49– (1963)
[5] DOI: 10.2307/1269553 · Zbl 0781.62154 · doi:10.2307/1269553
[6] Taguchi, Introduction to quality engineering: Designing quality into products and processes (1986)
[7] DOI: 10.2307/1270271 · Zbl 0800.62669 · doi:10.2307/1270271
[8] DOI: 10.2307/2685871 · doi:10.2307/2685871
[9] Harvey, Forecasting, structural time series models and the Kalman filter (1989)
[10] DOI: 10.2307/1270270 · doi:10.2307/1270270
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