| 研究生: |
廖大慶 Liao, Da-Ching |
|---|---|
| 論文名稱: |
制定統計容差界限時樣本數大小選取之探討與研究 Sample Size Determination for Setting up the Statistical Tolerance Limits |
| 指導教授: |
潘浙楠
Pan, Jeh-Nan |
| 學位類別: |
碩士 Master |
| 系所名稱: |
管理學院 - 統計學系 Department of Statistics |
| 論文出版年: | 2015 |
| 畢業學年度: | 103 |
| 語文別: | 中文 |
| 論文頁數: | 88 |
| 中文關鍵詞: | 統計容差界限 、六標準差 、樣本數 、權衡分析 |
| 外文關鍵詞: | Statistical tolerance limits, Six sigma, Sample size, Trade off analysis |
| 相關次數: | 點閱:241 下載:3 |
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統計容差界限在制定產品工程規格的過程中扮演著重要的角色,係肇因於工程規格對製程能力指標之計算有決定性之影響。幾十年來,已有多位學者提出在常態分配與非常態分配下統計容差界限的演算法。若產品品質特性之資料服從常態分配時,我們乃針對常態分配下不同的演算法作一比較並制定出符合現況之統計容差界限係數表。若產品品質特性之資料並非常態分配時,我們先利用Kolmogorov-Smirnov檢定判斷其品質特性資料屬何種特定之機率分配,若無適當的機率分配可配適,則我們改以無母數統計方法處理之。此外,在顧及工業界製造與組裝的現況下,我們將統計容差界限加入六標準差的考量而予以修正並進一步針對樣本數與涵蓋率之取捨作權衡分析。
最後,我們將研究成果加以整理並撰寫制定統計容差界限之標準作業流程,並以三個數值實例對上述方法作一驗證與說明,研究成果可提供業界在制定統計容差界限時之參考及使用。
The statistical tolerance limits plays an important role in determining product’s engineering specifications due to the fact that the engineering specifications will cause crucial effects on the calculation of process capability indices. Over the decades, several researchers have proposed the algorithms for computing statistical tolerance limits under normal distribution and non-normal distribution. For the situation that the quality characteristic follows normal distribution, we compare all the possible algorithms under normal distribution and then develop a table of statistical tolerance limits corresponding to the current manufacturing situation in industry. For the situation that the quality characteristic does not follow the normal distribution, we firstly use Kolmogorov-Smirnov test to determine the appropriate fitted distribution; if there is no suitable fitted distribution, we apply the nonparametric statistical method to resolve it. In addition, concerning the current manufacturing situation in industry, we add the Six Sigma consideration during the setup of statistical tolerance limits and further perform the trade-off analysis between sample size and yield rate.
Finally, we summarize the research results and propose a standard operating procedure for determining the statistical tolerance limits. Three numerical examples are also given to demonstrate the usefulness of our proposed approach. Hopefully, the results of this research can be served as a valuable guideline and references for manufacturing industries to set up statistical tolerance limits.
中文部分
1.潘浙楠(2009),“品質管理:理論與實務”,華泰文化。
2.潘浙楠、陳文欽(1999),“非常態分配下統計容差制定問題之探討與研究”,品質學報,第六卷,第二期,51-73頁。
英文部分
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18.Young, D. S. and Mathew, T. (2014). “Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics,” Journal of Nonparametric Statistics, Vol. 26, No. 3, pp. 415-432.