非常態分配數據轉換之研究

A Research of Non-Normal Distribution Data Transformation

劉玫瑰(Mei-Kuei Liu)

指導教授 ： 鄭春生

元智大學/工程學院/工業工程與管理學系/碩士(2004年)

摘要

現今製造業在實施統計製程管制時，大多使用管制圖與製程能力指標於品質的監控上，由於管制圖與製程能力指標的應用需建立在常態分配的基本假設上，因此，有必要確認製程中的數據是否為常態分配。本研究是利用統計軟體模擬不同的數據分配型態、參數和樣本大小來進行非常態分配數據轉換的研究與分析。當製程數據經過常態性檢定為非常態分配時，會因為非常態分配的數據應用於常態分配基礎之統計方法上，造成管理者或使用者做出錯誤的判斷與決策。因此，本研究之目的是為了要讓這些非常態分配的數據經過Box-Cox 轉換後，使之成為常態分配，再以此來進行數據的統計分析。
最後本研究共模擬了六種實際製程常見之直方圖分配型態，整理出轉換規則，並提供一個實務轉換的建議表，以符合實務業界使用上的參考依據。讓使用者對於實際製程上非常態分配的數據，能夠有一個判斷、分析的準則與適當的轉換方法，可供遵循與參考。

關鍵字

非常態分配 ； Box-Cox 轉換 ； 直方圖 ； K-S常態檢定

並列摘要

It is always seen nowadays that the control chart and process capability index are commonly put in use in quality control process by the manufacturers. Because the control chart and process capability index are both established on the assumption of normal distribution, it is a necessity to confirm whether the data collected from real manufacturing process is normally distributed or not. This research therefore emphasizes on simulating different distribution types, parameters and sizes of samples with statistic software. When the raw data shows non-normal distribution after regular testing, it often leads to wrong judgments or decisions by managers and end users when the data is not properly transferred into normal distribution. The main purpose of this research is to introduce the application of Box-Cox power transformation to transfer the non-normal distributed data into a new normal distributed pattern, and then further statistical and analytical could be available.
This study simulates six different common types of histograms in manufacturing process, and come up with transferring regulations which could lead to a practical transferring table for practical on-site applications. Finally these regulations could serve as a role model for transferring raw data into useful data which can be used by managers and end users for proper judging and appropriate decision making.

並列關鍵字

Non-normal distribution ； Box-Cox power transformation ； Histograms ； Kolmogorov-Smirnov test

參考文獻

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