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- Title
THE EXACT RUN LENGTH DISTRIBUTION AND DESIGN OF THE S<sup>2</sup> CHART WHEN THE IN-CONTROL VARIANCE IS ESTIMATED.
- Authors
CASTAGLIOLA, PHILIPPE; CELANO, GIOVANNI; CHEN, GEMAI
- Abstract
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 σ0 or variance $\sigma_0^2$ 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 $\sigma_0^2$. In this paper, we derive the exact run length distribution of the S2 control chart when the in-control process variance $\sigma_0^2$ 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.
- Subjects
STANDARD deviations; STATISTICAL process control; STATISTICAL quality control; ESTIMATION theory; VARIANCES
- Publication
International Journal of Reliability, Quality & Safety Engineering, 2009, Vol 16, Issue 1, p23
- ISSN
0218-5393
- Publication type
Article
- DOI
10.1142/S0218539309003277