監控線性趨勢製程之研究

Abstract

近年來，在製造工業界裡，某些製程可能會因為工具磨損、操作員疲勞、原料劣化等因素，導致製程呈現某種趨勢。然而此現象是無法避免的，我們必須把造成此種趨勢的原因視為機遇原因，並非可歸屬原因，所以若使用一般的管制圖來監控，會太早出現製程失控的假警報，導致不必要的成本增加。 目前已有多位研究學者提出了許多有關工具磨損製程的監控計劃，針對此種製程訂出了數種不同的工具汰換策略。然而現今的生產過程逐漸邁向自動化，對產品的要求也越來越高，在原本正常的趨勢製程裡，可能會因為某種可歸屬原因，例如不正常的工具汰換、換新操作員、異常的原料更換等因素，而導致製程發生了異常線性偏移的情況。本研究著重於管制圖在此種製程的偵測力，計算出Shewhart和EWMA兩種管制圖在不同偏移程度下的平均連串長度，並比較這兩種管制圖的偵測效率，進而找出一套有效的監控計劃，供業界在監控此種製程時作為參考。 在偵測出製程偏移後，最關心的往往是此偏移製程的可歸屬原因為何，於是本論文也針對此問題做了深入的探討。利用模型選擇方式來找出此偏移製程的模型，推論何種參數發生了偏移，進而找出可歸屬原因。近年來已有多位學者提出許多不同的選取準則來選擇模型，這些模型選取準則各有其適用性，因此本研究在眾多準則中，找出一套較適用於我們問題的準則，並分析其選取正確率，供業界在處理此種異常線性偏移資料的參考。

In many manufacturing processes, it is fairly common that the quality characteristic of interest exhibits a trend due to, say, tool wearing, material replenishing, machinery fatigue, etc. Unfortunately, this deteriorating trend is inevitable and is part of the system. Take tool wearing as an illustrative example: as the machining operation continues, tools wear gradually, which deteriorates the quality of the product/process and may eventually cause the product items out of specification. Hence, a proper control on tool wearing is necessary. Most of the tool-wear control focus on tool replacement, trying to set a policy to replace the tool at appropriate times that is cost-effective while keeping product items in spec. In this thesis, we study controlling processes with linear trend from the aspect of statistical process control (SPC) and focus on Phase II process monitoring. The main objective of SPC process monitoring is to keep the process in statistical control, which can be achieved by using control charts to detect process shifts and then find/eliminate the corresponding assignable causes. Since the trend is inevitable and systematic, it should be viewed as a common cause of process variation instead of as an assignable cause. Thus, when implementing a control chart for such processes, it is necessary to adjust charts for the linear trend to avoid unwanted out-of-control signals due to the trend. Assume the in-control linear trend is available. We first adjust the quality characteristic by this in-control linear trend and then apply the ordinary Shewhart chart and EWMA chart on the adjusted quality characteristic to monitor the process. We compute and compare the average run length (ARL) of these two control charts for various shift sizes of the intercept and/or slope. It is well known that the Shewhart chart is good for detecting large shifts while the EWMA chart is more sensitive to small shifts. By computing the range of the shifts for which the EWMA chart with the smoothing parameter has a better detecting power in terms of the ARL than the Shewnart chart, we provide a chart that can help engineers to choose between the two charts, if they know roughly where the process shifts might be. Moreover, when a process shift is detected by the chart, for diagnosis purpose, we provide a model selection technique to help engineers to determine whether the shift is on intercept or slope or both. Finally, we illustrate the applicability and effectiveness of the proposed scheme with a real-life tool-wear example.