結合指數加權移動平均與累和管制圖在監控多階段系統製程品質上之應用研究

Monitoring the Process Quality for Multistage Systems Using New Mixed EWMA-CUSUM Control Chart

潘浙楠(Jeh-Nan Pan) ； 李俊毅(Chung-I Li) ； 楊智榮(Jhih-Rong Yang)

《中國統計學報》 57卷3期 (2019/09) Pp. 232-262

摘要

隨著時代的進步，現今產品的製造過程愈趨精密、複雜；許多產品往往需要經過多個階段的製造流程才能順利完成。爲了更有效監控多階段系統製程品質，我們提出適合多階段系統使用的新殘差管制圖。在考慮多階段系統的製程中當階段常受前一階段相關性所造成之影響情況下，本研究採用Pan et al.（2016）所提出之多階段系統模型，先取得各階段模型的殘差值，再將所取得之殘差值代入混和指數加權移動平均與累和（Mixed EWMA-CUSUM）管制圖中並考慮快速初始反應值（Fast Initial Response，FIR）與Headstart，以期建立多階段系統新殘差混和EWMA-CUSUM管制圖（RMECFIRHS Chart，Revised Mixed EWMA-CUSUM Control Chart with modified FIR and Headstart）。接著，在各種參數組合下，我們以電腦模擬的方式進行管制圖偵測能力之比較並利用整體平均串長度（Overall Average Run Length, OARL）做爲多階段系統新殘差混和EWMA-CUSUM管制圖與Pan et al.（2016）之多階段系統殘差管制圖偵測能力的比較基準。最後我們以一筆三階段化學製造的資料爲例，進行數值實例的分析與探討。模擬結果與數值實例分析皆顯示本研究所提出之多階段系統新殘差RMECFIRHS管制圖的偵測能力均優於Pan et al.（2016）之多階段系統EWMA和CUSUM殘差管制圖。研究結果可做爲品管人員利用此種新管制圖在監控多階段系統製程品質時的參考。

關鍵字

多階段系統 ； 新殘差混和EWMA-CUSUM管制圖 ； 快速初始反應值 ； 整體平均串長度

並列摘要

With the advent of modern technology, manufacturing processes have become very sophisticated; most industries require multiple process stages to complete their final products. In this paper, we develop a new control chart model suitable for monitoring the process quality of multistage manufacturing systems. Considering the correlation often occurs among various stages in a manufacturing system, we first adopt the idea of multistage manufacturing systems model proposed by Pan et al. (2016) to establish a multistage residual RMECFIRHS (Revised Mixed EWMA-CUSUM with modified Fast Initial Response and Headstart) control chart. Then, a simulation study is conduct to evaluate the detecting ability of our proposed multistage residual RMECFIRHS control chart under various combinations of process shifts. The overall average run length (OARL) is used to compare the detecting performances of our proposed multistage residual RMECFIRHS control chart with those of multistage residual EWMA and CUSUM control charts. Finally, a numerical example of a three-stage with chemical manufacturing process is given to demonstrate the usefulness of our proposed multistage residual RMECFIRHS control chart. Both the simulation results and numerical example show that the detecting ability of our proposed multistage residual RMECFIRHS control chart outperforms the multistage residual EWMA and CUSUM control charts when a process shift occurs. Hopefully, the results of this research can be served as a useful guideline for monitoring the process quality of multistage systems.

並列關鍵字

Multistage manufacturing system ； Revised mixed EWMA-CUSUM control chart ； Fast initial response ； Overall average run length

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