摘要
為了迎合消費者需求以提升產品競爭力，許多科技產品越來越精密，其製造所需的時間以及成本也越來越高。因此，基於成本及其他因素的考量，監控製程的抽樣有時只能得到一個觀測值，此時產生了自由度不足以直接估計製程變異數的問題。本文主要是探討在資料服從常態分配的假設下，如何利用單一觀測值來對製程進行監控。Reynolds和Stoumbos (2001)比較了各種單一觀測值管制圖的組合表現，得到了最好監控效果組合的結論。我們將Shu與Jiang (2008)提出的監控製程變異數的方法，推廣到合理子群僅有一個觀測值的情況，並且另外提出幾個方法與上述二個方法進行比較。比較後發現，我們所提出的一種管制圖在監控製程變異數變大時有較好的表現，而另一種管制圖在監控製程變異數變小時有較好的表現，在同時監控製程平均數以及變異數偏移上，我們所提出的合併管制圖對整體的製程監控有相當不錯的表現。另外，我們也探討了所提出的合併管制圖對於估計改變點的準確度，並且利用估計得到的改變點將資料分群，進行可歸屬參數偏移的診斷。

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