改善之新開發製程自啟動管制程序

Abstract

建構管制圖監控系統包含兩個階段：第一階段(Phase I)是針對品質特性所蒐集的歷史資料建立管制圖，利用管制內之資料來估計製程參數，再以這些製程參數之估計值來建立管制界限，以供第二階段(Phase II)監控製程之用。然而許多新開發的產品或製程，缺乏足夠建構Phase I管制界限之資料，尤其是產品市場生命週期短、不斷推出新產品、不斷研發新製程的產業型態以及工作站(Job shop)生產型態的製程(又稱為Start-Up製程)更是如此。近年來已有研究發展出Q統計量管制圖來監控Start-Up製程是否發生偏移，Q統計量管制圖為自啟動(Self- Starting)管制程序，以running的方式動態地估計製程之變異及製程平均值，再利用估計之製程變異及平均值將各期的製程觀測值標準化，然後轉成Q統計量，再利用Q統計量繪製管制圖來監控製程。但在Self- Starting的管制程序中，當製程平均值發生偏移(mean shift)時，容易高估製程變異，而使得管制圖偵測製程平均值發生偏移之能力變差，現有之中外文獻大多只利用一些管制圖技巧或其他管制圖，如：連串測試法則、CUSUM及EWMA等來增加Q統計量管制圖監控製程之能力，也有文獻從改善高估製程變異方面著手，但成效有限。因此，本研究針對此Q統計量管制圖高估製程變異之情形，提出修正之Q統計量管制圖，提出以滾動分群(Rolling grouping)方式來準確地估計製程變異，以降低Q統計量管制圖之型二誤差，進而提昇管制圖偵測製程平均值發生偏移的能力。最後，本研究透過模擬實驗驗證了本研究所提出之方法確實比傳統的Q統計量管制圖及修正之Q統計量管制圖有效。

There are two distinct steps (namely, phases I & II) for constructing control charts. In phase I, preliminary samples of the process are necessary for estimating the process parameters and also for computing the control limits. Phase I control chart should ensure that process is in-control before starting phase II control chart. In phase II, control charts are used to monitor future process. However, in the initial stage of process settings, it is impossible to assemble preliminary samples. Such a process is called Start-Up process. Recently, some self-starting control scheme have been proposed for a Start-Up process. Q statistic control chart is one of the tool to monitor the Start-Up process in Self-starting control scheme. For the purpose of estimating process parameters, Q statistic utilizes running mean and standard deviation of all observations collected from the process since the process started. Q statistic is identically and independently distributed N(0,1) variables. Q statistic is used as the input data for online control chart to monitor the process. Many researchers have indicated that the process variance would be overestimated when mean shift occurs. This increases the type II error of the control chart. Hence, this study proposes a revised Q statistic control chart to improve the disadvantage of overestimating process variance by the traditional Q statistic. This study groups the observations based on the shift patterns of sample mean, called “Rolling grouping method” to accurately estimate the process variance. The effectiveness of the proposed method was demonstrated using a simulated case.