多變量JS管制圖

Abstract

對於多個變數的管制圖，這篇論文探討如何改進階段一參數估計來建立更精確的階段二管制界限。利用文獻上已證明，當多維度常態分配的平均數未知時，在平方損失的情況下，若變數維度高於2，一般常使用的樣本平均數估計量具有不容許性。許多的收縮估計量已經被證明比傳統估計量有更好的表現，例如 James-Stein估計量。在低損壞或高良率的製程，我們可使用 James-Stein估計量來改進階段一的參數估計。這篇論文提出利用改進估計量來構造多維度管制界限。利用電腦模擬和數值計算的結果顯示調整過後的管制界限比現有的管制界限有明顯的改進效果。

In this study, we focus on improving Phase I study to construct more accurate Phase II control limits for multivariate variables. For a multivariate normal distribution with unknown mean, the usual mean estimator is known to be inadmissible under the squared error loss when the dimension of variables is greater than 2. Shrinkage estimators, such as the James-Stein etc., are shown to have better performance than the conventional estimator in the literature. When considering a low defect or high yield process, we utilize the James-Stein estimator to improve the Phase I parameter estimation. Multivariate control limits based on the improved estimator are proposed in this study. The adjusted control limits are shown to have substantial improvements than the existing control limits.