Variable sampling interval Hotelling's T² chart with sampling at fixed times

Abstract

This study applies a sampling at fixed time feature to the variable sampling interval (VSI) Hotelling's T ² chart for rational subgroups. This control chart is called variable sampling interval with sampling at fixed times (VSIFT) control chart, in which the modification allows one to take additional samples between two fixed equally spaced time points when there is some indication of process mean shift for the multivariate process. From a practical viewpoint, the VSIFT control chart is easier to administer than the adaptive sampling interval control charts, i.e. VSI, variable sample size and sampling interval (VSSI), and variable parameters control charts. Numerical comparisons show that the VSIFT Hotelling's T ² chart performs better than the VSI, variable sample size, VSSI, variable parameters, and variable sample size and control limit Hotelling's T ² charts for detecting moderate and large shifts in the process mean in terms of the steady-state average time to signal.

本研究採用固定時間點抽樣於變動抽樣間隔 Hotelling's T ² 管制圖 ， 即以合理樣本來抽樣。 这管制圖稱為 VSIFT 管制圖。 若懷疑多變量製程可能發生變動時 ， VSIFT 管制圖則可以在固定時間點之間抽取附加樣本數。 從實務上的考量 ， 相對於其他的變動抽樣間隔適應性管制圖 (如: 變動抽樣間隔管制圖、 變動抽樣間隔和樣本數管制圖與變動參數管制圖) ， VSIFT 管制圖則容易於實務界來實施。 研究顯示以調整後平均訊息時間 (steady-state average time to signal) 為統計績效指標 ， VSIFT Hotelling's T ² 管制圖相較於其他的 Hotelling's T ² 適應性管制圖 (如: 變動抽樣間隔管制圖、 變動樣本數管制圖、 變動抽樣間隔和樣本數管制圖、 變動樣本數和管制界限管制圖與變動參數管制圖) 能更快偵測出製程平均數小至大幅度的跳動。

(聯絡人: [email protected])

Keywords:

• Hotelling's T ² chart
• sampling at fixed times
• average time to signal
• variable sampling interval

Keywords:

• 關鍵詞： Hotelling's T ² 管制圖 ， 固定時間點抽樣 ， 平均訊號時間 ， 變動抽樣間隔

Notes

(聯絡人: [email protected])