統計製程管制（Statistical Process Control，簡稱SPC）是監控製程品質特性的重要方法。透過管制圖（Control Charts）的監控，吾人能夠迅速地偵測出非機遇原因何時發生或是製程何時改變，再予以即時的修正即可防止不良品之產生，並減少不必要的品質損失。傳統的前置管制圖係建立在常態分配之基本假設之下，將規格寬度均分為四等分界定其管制區域，但當製程為非常態分配時，此設定方法之適用性則有待商榷。
本研究乃針對非常態分配前置管制界限（警戒線）之設定準則提出二種新的設定方法，即中位數二分法及眾數二分法，並探討非常態分配中常見之伽碼分配、韋伯分配、指數分配及對數常態分配在不同之偏態係數下，與傳統之規格寬度四分法間之差異，至於前置管制圖在不同設定方式下判異準則之有效性，吾人則利用型I誤差、平均串長度（ARL）配合製程能力指標進行評估。此外，本研究尚利用Box-Cox常態轉換法配合Bootstrap方法，針對非常態分配之製程進行轉換，結果發現上述四種非常態分配之製程經轉換後，因其誤警率過高，故常態分配下之設定準則均不適用於資料轉換後之製程監控。
最後，吾人針對當製程為非常態分配時，前置管制界限（警戒線）設定準則之選取方式依比較分析之結果彙製成表以供業界參考使用。

Good quality of products is the key factor of business success. With the advent of high-technology era, manufacturing process becomes more sophisticated and the normal assumption is not always valid. Due to its simplicity and easy-to-use, the pre-control chart has been regarded as a very popular tool for process control, especially in the machine shop during the 1980s when S.P.C. becomes fashionable again. However, the simple rules of the pre-control chart are no longer suitable for the sophisticated manufacturing process when non-normal quality characteristics involved.

Therefore, the purpose of this research is to investigate and develop the appropriate rules for pre-control charts under non-normal distribution. We propose two methods: bisection method using median, and bisection method using mode for setting up the pre-control chart under non-normal distribution such as: Gamma, Weibull, and Lognormal distributions. Similar approaches then will be extended to compare the performance of pre-control charts under different setting-up methods. Type I error and Average Run Length (ARL) are used as criteria to evaluate their performance in conjunction with the process capability indices. Moreover, the Box-Cox transformation and Bootstrap methods are also used to convert the non-normal data to normal data and then apply the traditional setting-up method to pre-control charts. The results show that the above method is not adequate due to the high false alarm rate.

Finally, a summary table of decision rules will be established based on the results of computer simulations and comparative studies for both normal and non-normal pre-control charts. Hopefully, it can provide a useful reference for the industries.

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