在使用管制圖對製程品質特徵分佈的平均數與變異數參數同時進行監控時，在未知真實參數下通常需要大量的第一階段管制狀態資料來對參數進行估計並用以建構管制界限，但在實際情形下管制狀態資料的數量通常都較為有限。Zamba 和 Hawkins (2005) 提出了利用概似比做為監控統計量的改變點偵測管制圖，可在線上監控的同時不斷更新參數的估計值，因此對第一階段管制狀態下資料數量的需求較低，且在管制圖發出失控警訊的同時，可得到改變點的估計值。該方法可同時監控平均數和變異數，但在管制圖發出失控警訊後，需要額外進行後續的統計檢定來診斷參數是否發生改變。本文提出使用不同監控統計量的改變點偵測管制圖，利用兩組樣本之t檢定和F檢定的檢定統計量經逆轉換後之最大值來同時監控兩個參數，可在管制圖發出失控警訊的同時對改變參數進行診斷。此外，也結合了兩種EWMA機制來改善當製程參數改變量較小時監控效力較差的問題。我們以統計模擬將所提的監控方法與 Zamba 和 Hawkins (2005) 的方法進行比較，發現我們所提出的管制圖在大部分情況下有較好的監控效力。最後我們透過一筆金礦採樣的含金量比資料來說明實際上該如何使用所提出的管制圖。

When using control charts to monitor the mean and variance of the distribution of a process quality characteristic simultaneously, if the in-control parameters are unknown, usually a big amount of Phase I in-control data is needed to estimate the parameters. However, to collect many in-control data is not practical in the real world. Zamba and Hawkins (2005) proposed a change-point detection chart that uses the likelihood ratio as the charting statistic for monitoring the process mean and variance simultaneously. Their chart can keep updating the parameter estimates and also can estimate the change point at the same time while an out-of-control signal triggers. However, their method still needs additional statistic tests to identify which parameters cause the signal. In this article, we use a different monitoring statistic to construct a new change-point detection chart, that is, we use the maximum of the inverse transformations of the t and F test statistics to monitor the two parameters simultaneously. In this way, we can estimate the change point and identify the shifted parameter immediately when the chart has an out-of-control signal. In addition, we incorporate two types of EWMA mechanisms into the proposed chart to improve the monitoring efficiency when the shift size of the parameter is small. Comparisons between the proposed chart and Zamba and Hawkins (2005) are conducted by statistical simulations, and we find that the proposed chart has better monitoring efficiency in most out-of-control situations. At last, we use a set of data of ratios of gold content in successive samples to demonstrate how to apply the proposed chart to real data.

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