When monitoring the process variability, it is a common practice that a Phase I data setis used to estimate the unknown in-control process standard deviation or variance 20to set up the control limits, then monitoring proceeds. Once the process is considered tobe in-control, the estimated control limits are assumed as fixed. This practice ignores theeffect of estimating the unknown in-control process variance. In this paper, we derivethe exact run length distribution of the S2 control chart when the in-control processvariance is estimated and find that m = 200 or more Phase I samples are needed toneglect the effect of using estimated control limits. New control limits when m is smallare also derived.

The exact run length distribution and design of the S2 chart when the in-control variance is estimated

CELANO, GIOVANNI;
2009-01-01

Abstract

When monitoring the process variability, it is a common practice that a Phase I data setis used to estimate the unknown in-control process standard deviation or variance 20to set up the control limits, then monitoring proceeds. Once the process is considered tobe in-control, the estimated control limits are assumed as fixed. This practice ignores theeffect of estimating the unknown in-control process variance. In this paper, we derivethe exact run length distribution of the S2 control chart when the in-control processvariance is estimated and find that m = 200 or more Phase I samples are needed toneglect the effect of using estimated control limits. New control limits when m is smallare also derived.
2009
Process variance; s2 control chart; conditional distribution
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/27014
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