給定兩個實驗次數相同的二水準因子設計，令D_1和D_2分別表示它們的設計矩陣。考慮另一個實驗次數相同的設計D^(r)，其由D_1與D_2^(r)列與列合併而成，其中D_2^(r)表示 D_2 經過某種列互換 r 後所得的矩陣。我們稱D^(r)為逐列合併設計。本研究探討已知D_1及D_2之計數函數的情況下，D^(r)的計數函數與它們之間的關係。首先我們透過D_1, D_2列與列之間的映射關係以及對計數函數的係數做分類兩種不同觀點，對D^(r)的計數函數進行討論，得出D^(r)的計數函數並不唯一的結果。接著我們限制D_1為D_2的子矩陣，在此條件下，推導出D^(r)的計數函數可被D_1, D_2之計數函數唯一決定，並發展出一些性質與應用。最後，假設已知D^(r)的計數函數，考慮對D_2^(r)某兩列作互換後再形成的新逐列合併設計D^(r')，我們藉由r與r'之間的關係來刻劃D^(r)與D^(r')的計數函數之間的關連性。

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