研究機率分佈的性質一直以來都是統計和應用機率領域的重要課題。Azzalini (1985) 提出的偏斜常態分佈，不僅涵蓋常態分佈，且具有一些與常態分佈相同的性質。此類分佈有助於穩健性的研究和偏斜性的建模。此後，便有許多人投入基於對稱分佈的偏斜分佈之研究。本論文將完整地探討所謂的偏斜常態均勻分佈，除了基本性質外，也將探討其點估計和平均數之分佈。偏斜常態均勻分佈不但可比典型且被廣泛討論的常態分佈更具彈性，亦提供不同於Azzalini之偏斜常態分佈的偏斜模型選擇。在應用方面，我們將探討此偏斜常態均勻分佈在品質管制圖的制定上，以期提供一個可用且有效的統計模型來處理非對稱資料，並改善修華特管制圖無法達到監控非對稱資料的目的。

The study of properties of probability distributions has always been a persistent theme of statistics and applied probability. Azzalini (1985) introduced the skew-normal distribution which includes the normal distribution and has some properties like the normal and yet is skew. This class of distributions is useful in studying robustness and for modeling skewness. Since then, skew-symmetric distributions have been proposed by more authors. In this thesis, we study the so-called skew-normal-uniform distribution, which is flexible than the normal distribution and different from Azzalini's skew-normal distribution. Explicit forms of its c.d.f. and moments are derived. The method of moments estimation and the maximum likelihood estimation of location-scale skew-normal-uniform distribution are discussed. We also study the distribution of the sample mean and then study control charts for the skew-normal-uniform distribution to monitor the process average of non-normal data. This improves the defect of Shewhart control chart and provides an effective model to deal with the non-normal data.

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