整合EWMA管制圖降低R2R製程控制次數之研究

Combining EWMA Control Chart to Reduce Process Control Frequency for Run-to-Run (R2R)

江行全(Bernard C. Jiang)；王建智(Chien-Chih Wang)；任志宏(Chih-Hung Jen)；羅列強(Lie-Ciang Luo)

EWMA管制圖 ； R2R控制器 ； bootstrap估計 ； EWMA control chart ； R2R control ； bootstrap method

品質學報

16卷4期（2009 / 08 / 31）

233 - 243

繁體中文

傳統R2R(Run to Run)控制程序，每一個run皆需進行控制。但這種控制程序將產生許多不必要的控制成本，並可能產生過度控制(over control)的情況。基於這個原因，本研究加入EWMA管制圖做爲調整界限的設定準則，藉以判斷控制系統是否需要啓動。當製程反應值超出調整界限時，控制器立即啟動並針對下一個run偏離目標值的情形進行參數調整。由分析結果顯示，結合調整界限的控制機制，在製程反應值變異未增加的狀況下，可使製程所需調整的次數約減少50%。此外，本研究結合bootstrap法則估計出傳統R2R控制在不同參數組合下反應值(y(下標 t))MSE的信賴區間，並利用此信賴區間測試本研究方法與傳統R2R控制在MSE上是否有顯著性的差異，結果顯示兩者的控制結果並無顯著差異。藉由以上的操作。本研究所提出的控制方法確實能夠有效地降低製程調整次數，並且也能夠避免過度控制的發生及降低控制成本。

In traditional R2R scheme, the controller compensates for a variety of noise disturbances so that the process output of each run can maintain as close to the nominal target as possible. But this control has a problem, that is, if all of runs are executed the parameter adjustment that the process is likely to generate the situation of ”over control”. In views of this, the research used the control limit concept in EWMA control chart to evaluate whether the controller should be started. When the process output exceeds this adjustment threshold, the controller is started to regulate the process parameter so that the next run is able to on target. From the simulated results, if this control framework can be used that the adjusted numbers would be able to reduce approximately 50%, and does not increase the output variability. Moreover, using the bootstrap method the confidence interval of the mean squares error (MSE) of the outputs (y(subscript t)) can be constructed in the different parameter composing. In terms of this confidence interval, we can test the MSE values between the proposed framework and the traditional R2R control and judges whether to exhibit a significant difference. Using this test it can be found that the proposed control framework is indeed able to decrease the adjusted numbers, and it can also prevent the situation of the 'over control'.

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