When monitoring the process variability, it is a common practice that a Phase I data set is used to estimate the unknown in-control process standard deviation or variance 2 0 to set up the control limits, then monitoring proceeds. Once the process is considered to be in-control, the estimated control limits are assumed as fixed. This practice ignores the effect of estimating the unknown in-control process variance. In this paper, we derive the exact run length distribution of the S2 control chart when the in-control process variance is estimated and find that m = 200 or more Phase I samples are needed to neglect the effect of using estimated control limits. New control limits when m is small are also derived.
|Titolo:||The exact run length distribution and design of the S2 chart when the in-control variance is estimated|
|Data di pubblicazione:||2009|
|Appare nelle tipologie:||1.1 Articolo in rivista|