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系統識別號 U0026-0907201814251500
論文名稱(中文) 製程品質有輔助資訊時一個新指數加權移動平均管制圖之制定與研究
論文名稱(英文) Developing a New FIR-EWMA Control Chart for Monitoring the Process Quality with Auxiliary Information
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 106
學期 2
出版年 107
研究生(中文) 鄭惠文
研究生(英文) Hui-Wen Cheng
學號 R26054056
學位類別 碩士
語文別 中文
論文頁數 52頁
口試委員 指導教授-潘浙楠
口試委員-鄭春生
口試委員-李俊毅
中文關鍵字 指數加權移動平均管制圖  快速初始反應  Product Estimator  Ratio Estimator  平均連串長度 
英文關鍵字 Exponentially weighted moving average  Fast initial response  Product estimator  Ratio estimator  Average run length 
學科別分類
中文摘要 製造業者在蒐集產品製程中所感興趣的關鍵品質特性資料時,也會蒐集一些與製程有關的其他輔助訊息。Cochran(1940) 提出當兩個品質特性為正相關時, Ratio estimator 能較精確地估計出品質特性之值;另一方面,Robson(1957) 提出 Product estimator,可用來估計品質特性與輔助訊息呈負相關時的情況。近年來陸續有學者針對感興趣的品質特性與輔助變數間的關係進行研究。Adegoke et al.(2017) 以及 Sanusi et al.(2017) 曾分別運用 Product estimator 及 Ratio estimator 提出指數加權移動平均管制圖。然而彼等所提出之指數加權移動平均管制圖僅在輔助變數的變異係數與兩倍品質特性的變異係數之比值小於或等於相關係數的絕對值時,此管制圖的偵測能力才優於傳統的指數加權移動平均管制圖。
本研究係藉由加入快速初始反應值的想法,並根據相關係數的轉換取得新的快速初始反應值之計算方式,建立了加入快速初始反應的新指數加權移動平均管制圖 (Fast Initial Response-Exponentially Weighted Moving Average control chart, FIR-EWMA chart)。接著,我們使用平均連串長度 (ARL) 以模擬的方式來比較本研究所提出的 FIR-EWMA chart 與 Adegoke et al.(2017) 之 EWMA_P chart 以及 Sanusi et al.(2017) 之 MrEWMA chart 在偵測能力上的優劣。結果發現當關鍵品質特性的製程平均發生改變時,FIR-EWMA chart 較能及早偵測到製程的異常。最後,我們以 Marlin(2000) 文中非等溫連續攪拌釜化學反應器 (CSTR) 的資料集進行數值實例的驗證與說明,本研究結果未來可供製造業者在監控關鍵品質特性時的參考。
英文摘要 The SPC control charts play an important role in monitoring and improving the process quality. Generally speaking, when the key quality characteristics of interest are measured, auxiliary information other than the key quality characteristics are also collected. Cochran(1940) pointed out that ratio estimator can accurately estimate the value of quality characteristics when two quality characteristics are positively correlated. Robson(1957) found that product estimator which can be used to estimate the quality characteristics that has a negative correlation coefficient between auxiliary information. Recently, some researchers have studied the control chart for monitoring the quality characteristics of interest with auxiliary variables. The EWMA_p (proposed by Adegoke et al.,2017) and MrEWMA charts (proposed by Sanusi et al.,2017) are based on product estimator and ratio estimator respectively. However, EWMA_p and MrEWMA charts perform better than the classical EWMA only when the ratio of the coefficient of variation of the auxiliary information to the coefficient of variation of the double quality characteristic is less than or equal to the absolute value of the correlation coefficient.
Thus, we adopt the idea of adding the fast initial response value to establish a new Fast Initial Response-Exponentially Weighted Moving Average control chart (FIR-EWMA chart). A simulation study has been conducted to evaluate the detecting ability of our proposed FIR-EWMA chart. We compare the detecting performance of our proposed FIR-EWMA chart with that of both EWMA_p and MrEWMA charts by using the out-of-control average run length (ARL_1). Finally, a CSTR (nonisothermal continuous stirred tank chemical reactor) data set is given to demonstrate the usefulness of our proposed FIR-EWMA chart. Both the simulation results and numerical example show the detecting ability of our proposed FIR-EWMA charts outperforms EWMA_p and MrEWMA charts when a process shift occurs.
論文目次 第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究架構 3
第二章 文獻回顧與探討 5
2.1 Ratio Estimator 5
2.2 Product Estimator 6
2.3 指數加權移動平均管制圖 7
2.4 MrEWMA 管制圖以及 EWMA_P 管制圖 9
2.5 快速初始反應指數加權移動平均管制圖 11
第三章 新快速初始反應指數加權移動平均管制圖之建構 13
3.1 快速初始反應 13
3.2 新快速初始反應的訂定 14
3.3 假設相關性為正建構新快速初始反應指數加權移動平均管制圖 16
3.4 假設相關性為負新快速初始反應指數加權移動平均管制圖之建構 17
第四章 統計模擬分析 19
4.1 管制圖績效的評估 19
4.2 統計模擬之設定 20
4.3 模擬結果 23
第五章 數值實例分析 31
5.1 資料介紹及參數估計 31
5.2 相關係數為正之情形下的實例分析 33
5.3 相關係數為負之情形下的實例分析 38
第六章 結論與未來研究方向 43
6.1 結論 43
6.2 未來研究方向 44
參考文獻 45
附錄 47
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