管制圖經常是在常態假設下被設計，但是在某些製造過程中，常態假設經常無法成立。Tsai [12]提出一個偏常態平均數管制圖來監控非常態資料的平均數。他顯示此一管制圖可以有效地改進目前一些已知的管制圖在此一問題平均數監控上的效果。本文以偏常態平均數管制圖為基礎發展出偏常態允收管制圖來監控非常態資料的製程平均數及不良品的比率。當測量值服從對稱分配時，此法可退化到一般的允收管制圖，本文也以兩個實例來舉例說明。由這兩個例子可以看到本文建議的允收管制圖可以很容易地建構，並且也可看出若忽略非常態性將提高管制圖第一型及第二型錯誤的機率。

Control charts often are designed under the normality assumption. But in some manufacturing processes this assumption may not be valid. Tsai [12] developed a skew normal (average) X (subscript L) control chart to monitor the process average for non-normal data. He showed that a considerable improvement over those of existing control charts can be achieved when the skew normal (average) X (subscript L) control chart is used to monitor the process average. Based on the skew normal (average) X (subscript L) control chart, the paper develops a skew normal acceptance control chart to monitor the process average and the fraction of nonconformities for non-normal data. The proposed acceptance control chart reduces to the conventional acceptance control chart as the underlying distribution of measurements is symmetric. Two examples are given for illustration. The presented examples show that the construction of the proposed acceptance control chart is easy, moreover, ignoring the non-normality effect will result in a higher type I or type II error probability.