傳統上，使用管制圖來監控製程，假設製程觀測值是獨立的分配。事實上，很多製程的產品不是具有關聯性就是具有自我相關性，因此，所獲得的觀測值是自我相關而非獨立的。在這種情狀下，利用獨立而非相關的假設去監控製程是不適當的。當相關性存在觀測值間，管制圖的表現可能造成某種程度的影響。特別是，產生較高的錯誤警訊。為了降低錯誤警訊的頻率和增加管制圖的偵測能力，本研究主要針對當觀測資料有顯著自我相關時，監控其製程的平均數與變異數的微小偏移。
在處理自我相關的資料時，一般有兩種方法建立其管制圖。其一，視觀測值為統計量製作廣泛加權移動平均(GWMA)管制圖並調整管制界線來監控一階自我迴歸(AR(1))模型加上一個隨機誤差項的相關性製程。透過數值的模擬來衡量觀測值的指數加權移動平均(EWMA)與GWMA管制圖的平均連串長度(ARL) 。透過ARL的比較顯示，觀測值的GWMA在低度相關時，偵測製程變異所需的時間比在高度相關時來的短。在偵測小偏移的製程平均數與變異數方
面，觀測值的GWMA比EWMA管制圖來的敏感。
此外，另一種方法是選取適當的時間序列AR(1)模型加上一個隨機誤差項，視配適模型後的殘差值為統計量來監控相關製程的平均數與變異數。殘差值的EWMA與GWMA管制圖被運用來監控製程的平均數與變異數並衡量其平均連串長度的差異。數值模擬的結果也顯示，在偵測小偏移的製程平均數與變異數時，殘差值的GWMA比EWMA管制圖敏感。

Traditionally, using a control chart to monitor a process assumes that process observations are normally and independently distributed. In fact, for many processes, products are either connected or autocorrelated and, consequently, obtained observations are autocorrelative rather than independent. In this scenario, applying an independence assumption instead of the autocorrelation for process monitoring is unsuitable. When autocorrelation exists between observations, the performance of control charts may cause dramatic influence. Specifically, a high number of false alarms signals are generated. In order to decrease the frequency of false alarms and increase detection ability of control chart, the main problem addressed in this study is to monitor small shifts in the process mean and/or variance for which
observational data meet significant autocorrelation.
Two general approaches to developing control charts can be adopted in cases of autocorrelation. One, a generally weighted moving average (GWMA) control chart of observations for monitoring a process is introduced and the control limits adjusted for the autocorrelated observations in which the observations can be modeled as a first-order autoregressive (AR(1)) process with a random error. Simulation is utilized to evaluate the average run length (ARL) of an exponentially weighted moving average (EWMA) and GWMA control charts of observations. Numerous comparisons of ARLs indicate that the GWMA control chart of observations requires less time to detect various shifts at low levels of autocorrelation than those at high of autocorrelation. The GWMA control chart of observations is more sensitive than the EWMA control chart of observations for detecting small shifts in a process mean
and/or variance.
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