運用拔靴法建構非線性剖面製程監控之研究

Nonlinear Profile Monitoring Using a Bootstrap Approach

陳庚辰(Geng-Chen Chen)

指導教授 ： 范書愷

國立臺北科技大學/管理學院/工業工程與管理系碩士班/碩士(2014年)

https://doi.org/10.6841/NTUT.2014.00872

摘要

在統計製程管制的應用裡，隨著製程日趨複雜，產品的特性不再是由單一的品質特性來決定。在許多實際的製程中，製程或產品的品質特性是由反應變數以及一個或多個的解釋變數所呈現的函數關係來定義的。近幾年間，剖面製程監控的研究仍持續在進行中。
本研究提出一個方法運用於監控非線性剖面製程。在本研究中，我們採用參數方法監控回流焊處理過程的溫度曲線。首先，以Bootstrap(拔靴法)建置製程資料的信賴區間，接著分別以Polynomial Regression model(多項式回歸模型)、Sum of Sine(正弦波函數)、B-Spline model(B樣條)對製程曲線資料以及信賴區間配適，將模型的參數採用Hotelling’s T2統計量計算，並將信賴區間所計算的統計量當作管制界線對製程做監控。接著與使用B-Spline配適後產生之控制點(Control Points)做參數監控的方法做比較。在Phase I模擬階段，每一個模型皆有不錯的表現。在第二階段模擬結果本研究方法在監控製程異常之情況時的平均連串長度(ARLout)優於比較之方法。

關鍵字

統計製程管制 ； 非線性剖面 ； Bootstrap(拔靴法) ； Polynomial Regression model(多項式回歸模型) ； Sum of Sine(正弦波函數) ； B-Spline model(B樣條) ； Hotelling’s T2 ； 製程異常下平均連串長度(ARLout)

並列摘要

Lately, profile monitoring has drawn considerable attention in the Statistical Process Control (SPC) research field. This thesis proposes a new monitoring framework for the nonlinear profile data of the reflow process. First, the bootstrap method is applied to the limited profile samples to build up the confidence intervals. Subsequently, the polynomial regression, sum of sine and B-spline models are adopted to fit the obtained confidence bands. In the meantime, the parameter estimates in the fitted models are monitored by using the well-known Hotelling’s T2 control charts. Three approximating models will be compared for their fitting performance. In Phase I, all the studied models can correctly identify the outlying profiles of the reflow process data. In Phase II, the proposed monitoring method provides better out-of-control average run length (ARL) performances than the B-spline approximation approach.

並列關鍵字

SPC ； Nonlinear Profile ； Bootstrap ； Polynomial Regression model ； Sum of Sine ； B-Spline model ； Hotelling’s T2 ； Average Run Length (ARLout)

參考文獻

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