具估計管制界限之Shewhart X bar 管制圖被廣泛地應用。 當觀測樣本大小非固定時，我們提出七個估計標準差的統計量。 這些統計量被應用來估計 Shewhart X bar 管制圖的管制界限。 經由電腦模擬，我們得到上述估計量之值並進行比較及討論。 最後，經由模擬平均連串長度(ARL)，我們探討上述七個統計量在管制圖上的個別表現。

Shewhart X bar control charts with estimated control limits
are widely used in practice. When the sample size is not fixed,we propose seven statistics to estimate the standard deviation sigma . These estimators are applied to estimate the control limits of Shewhart X bar control chart. The estimated results through simulated computation are given and discussed. Finally, we investigate the performance of the Shewhart X bar control charts based on the seven estimators of sigma via its simulated average run length (ARL).

1.Introduction
2.The optimal linear combination
3.Applications to Shewhart X bar control charts
4.Conclusions and discussions

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The median absolute deviations and their applications to Shewhart X bar control charts.
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