工業界在進行各種品質改善的專案計畫與實務案例中，許多問題均牽涉到多個彼此相關反應值的要因分析。以本研究所探討之電路板塑料方型扁平式封裝(QFP)及球狀方陣封裝(BGA)為例，此種印刷電路板的焊接製程有四個彼此相關之品質特性，即焊接體積(deposited volume)、面積(deposited area)、高度(deposit- ed height)及焊接材料投入／產出的轉換比(transfer ratio)。Jianbiao Pan(2004)在電路板BGA及QFP焊接製程的要因探討一文中曾針對焊接體積及投入／產出轉換比之反應值，分別以全因子實驗(full factorial)方式進行模板厚度(stencil thickness)、焊接材料(solder paste type)、板之處理方式(board finish)、輸送帶速度(print speed)、模板孔徑大小(aperture size)及孔徑形狀(aperture shape)等六個製程參數的變異數分析，以分別找出其影響的重要因子。

由於上述QFP及BGA焊接製程中焊接體積、面積、高度及焊接材料投入／產出轉換比等四個反應值彼此相關，以個別反應值分別探討其影響要因的方式並不妥當，故本研究採用馬式距離結合田口系統之MTS(Mahalanobis-Taguchi system)及MTGS(Mahalanobis -Taguchi-Gram-Schmidt system)等多變量分析之手法，先將此種多重品質特性製程的反應值正交化，再利用馬氏距離的信躁比(signal to noise ratio)尋找要因。並將上述四種反應值 轉換成為希求度函數(desirability function， )後，利用其總希求度函數進行製程之最佳化。以期建立一種透過MTS／MTGS及希求度函數方式分析多重反應值製程要因的手法。最後本研究將此分析手法與傳統田口方法進行比較分析，結果顯示本研究所提出之方法較田口方法更能正確判斷出要因。

Multiple-input(factors) and multiple-output(response) problem has been frequently encountered and discussed in many quality improvement projects and case studies. For example, there are four correlated quality characteristics in the solder paste stencil process, i.e. the volume, area and height of solder paste deposited, which can be measured by an inline fully automatic laser-based 3-D solder paste inspection system. In addition, transfer ratio is another response variable used in the key factor analysis of solder paste stencil printing for quad flat package(QFP) and ball grid array(BGA) package. Jianbiao Pan(2004) conducted an experiment to determine which are the critical variables(factors) that control the amount of solder paste deposited and transfer ratio. Six factors selected in his study are stencil thickness, aperture size, aperture shape, board finish, solder paste type, and print speed.

This paper proposes a multivariate technique based on the Mahalanobis-Taguchi- Gram Schmit system(MTGS) as well as the desirability function to explore the key factors for the QFP / BGA solder paste stencil printing process. First, an integrated Mahalonobis-Taguchi system(MTS) as well as the MTGS technique are utilized to diagnose the abnormities of the above-mentioned QFP date and then the signal-to-noise(S / N) ratios are calculated for finding the key factors. Furthermore, four correlated response values are converted to their desirability functions in order to find an overall desirability function for the multi-response solder paste stencil printing process. Finally, both the analysis results of MTS / MTGS and Taguchi methods are compared. The results show that our proposed method is more accurate than Taguchi method in searching out the key factors.

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