摘要
摘要 本研究的目的即是針對自相關性製程作探討，我們將以ARTA過程來產生我們所需之自相關性資料，而所用到的管制圖包含：Shewhart管制圖、EWMA管制圖。而評估管制圖的績效指標為平均連串長度(Average Run Length；ARL)， 所以透過模擬實驗來估計當資料具有相關性時，我們使用管制圖卻忽略此性質所產生差異。和知道資料為相關性時修正管制圖後所產生的績效指標是否良好，且將以非常態分配資料去模擬其平均連串長度值。 當有自我相關性的存在時，它與傳統管制圖假設相違背，傳統管制圖的建構，常假設製程觀察值是獨立的，然而實務上確有許多情形違背此假設。在製程有自我相關性時，會造成管制內的ARL縮短，使得管制圖的誤警次數明顯增加。因此，解決自相關的問題，對於製程來說是非常的重要。 在我們實驗中，我們針對ARTA過程模擬產生相關性觀察值，ARTA是由AR透過函數轉換而得來，此方法可產生具指定邊際分配的相關性觀察值，邊際分配不限定於連續型或標準統計分配，因此可廣泛應用。在使用ARTA之前，必須透過數值積分法求解AR指定的相關係數值(Cario and Nelson 1998)。 根據我們實驗的結果發現：在相關性資料中，其資料為非常態配時，用EWMA管制圖跟Shewhart管制圖做監控，其穩健性是EWMA管制圖較好，而且選取的 值越小其穩健性越高，EWMA管制圖也比Shewhart管制圖更適用於偵測小製程的偏移上，尤其在偏移量為0.5~1內。
並列摘要
ABSTRACT The propose of this research is specific with autocorrelated production. We as-sume the measure of quality characteristic is a ARTA process. The control charts we consider include: Shewhart chart, EWMA chart. The control chart performance is av-erage run length, so we are use simulated experiments to estimate when data process has autocorrelated, but we overleap that. We want to realize the performance in re-vising control chart as the process is autocorrelated and use Non-normality data to simulated the average run length. But the independent character assumption in the data is violated, such a result, will make ARL while controlling shorten and cause mistake alert number of times made maps to in charge of increase obviously, Personnel will be make the mistakes in out of control to judge by accident. For our experiments, we consider the correlated data process such as ARTA process. ARTA process is a correlated stationary process that takes a base AR(Autoregressive) process with a desired marginal distribution and can be ap-plied widely. The values of AR autocorrelations are determined by the values of ARTA autocorrelations . Cario and Nelson(1998) propose the numerical search procedure to find the value of autocorrelations in AR which gives the target autocorrelations in ARTA. According to our experiment results, we find that: in autocorrelated data, when data process is Non-normality, use EWMA chart and Shewhart chart, the robustness of EWMA chart is better than Shewhart chart, and when we consider the robustness increase parameter decrease. The EWMA chart is more useful than Shewhart chart to suit a small process shift especially the shift is 0.5~1.
參考文獻
延伸閱讀
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