在模擬實驗中，我們通常需要考慮兩個重要的問題：一是如何選擇適當的績效衡量指標(performance measure)；決定了績效衡量指標之後，另一個問題便是如何決定績效衡量指標的品質(quality measure)。對於前者，我們通常以母體平均數作為績效衡量指標，以樣本平均數為其點估計(point estimator)。對於後者，我們通常以樣本平均數的變異數大小作為其品質指標，本論文就是研究這個問題。
針對一個自我相關穩態的模擬輸出序列(stationary process)，已有許多學者發表關於估計樣本平均數的變異數的方法，其中有許多估計樣本平均數變異數的估計式是以批量大小為參數的批量估計式。如何估計出最佳的批量目前仍是待解決的難題。
本論文目的乃是希望推導出一個理想的估計量，但避免直接估計最佳批量的途徑試以兩個批量估計式之線性組合模式為出發點，企圖尋求出最佳的線性組合係數以得到一個樣本平均數變異數的理想線性組合估計式。

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