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.File | Dimensione | Formato | |
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