An Alternative P-Value Test Approach to Tests of Mean for Normal Population with Fuzzy Data

新觀點之P值檢定法於模糊資料常態母體平均數的檢定

蔡長鈞(Chang-Chun Tsai) ； 陳正哲(Cheng-Che Chen)

《工業工程學刊》 22卷6期 (2005/11) Pp. 485-496

https://doi.org/10.29977/JCIIE.200511.0005

摘要

本研究建議一個新觀點之P值檢定法，在模糊資料下進行常態母體平均數之統計檢定。實務上，本方法可應用於製造環境中關於平均品質特性之檢定。在平均數之檢定中，由於母體變異數已知時之模糊檢定統計量與模糊資料的函數關係不同於母體變異數未知之情況，因此本研究根據模糊數之α截集分別建立模糊檢定統計量之歸屬函數，再由所得之歸屬函數計算出一個新觀點之P值，將此P值與顯著水準比較後即可下統計決策。最後，由兩個例子來說明本方法之應用。

關鍵字

模糊集合 ； 模糊數 ； 假設檢定 ； P值

並列摘要

This paper proposes an alternative p-value test approach to proceed statistical tests of mean for normal population with fuzzy data. In real-world applications, the approach is often used in tests of average quality characteristics in manufacturing environments. In the proposed approach, the membership function of fuzzy test statistic is first constructed based on the α-cuts of fuzzy numbers. Since the function relationship between fuzzy test statistic and fuzzy data under known population variance is different from that under unknown population variance, we use two methods to construct the membership function under known and unknown population variance environment respectively. An alternative p-value is then calculated according to this membership function. Consequently, a statistical decision can be made by comparing the alternative p-value with the significance level. Two numerical examples are given for illustration.

並列關鍵字

fuzzy sets ； fuzzy number ； hypothesis testing ； p-value

參考文獻

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