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系統識別號 U0026-0807201501412600
論文名稱(中文) 制定統計容差界限時樣本數大小選取之探討與研究
論文名稱(英文) Sample Size Determination for Setting up the Statistical Tolerance Limits
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 103
學期 2
出版年 104
研究生(中文) 廖大慶
研究生(英文) Da-Ching Liao
學號 R26021142
學位類別 碩士
語文別 中文
論文頁數 88頁
口試委員 指導教授-潘浙楠
口試委員-鄭春生
口試委員-溫敏杰
中文關鍵字 統計容差界限  六標準差  樣本數  權衡分析 
英文關鍵字 Statistical tolerance limits  Six sigma  Sample size  Trade off analysis 
學科別分類
中文摘要 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。
英文摘要 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.
論文目次 第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 2
第三節 研究架構 2
第二章 文獻回顧與探討 4
第一節 六標準差之意涵 4
第二節 自然容差界限 5
第三節 常態分配下的統計容差界限 5
第四節 非常態分配下的統計容差界限 10
第五節 無母數統計容差界限 14
第六節 制定無母數統計容差界限之樣本數選取 18
第三章 研究方法 19
第一節 常態分配下統計容差界限之設定 19
第二節 常態分配下統計容差界限設定樣本數大小之權衡分析 22
第三節 非常態分配下統計容差界限設定之模擬方法 25
第四節 非常態分配下統計容差界限設定樣本數大小之權衡分析 30
第五節 無母數統計容差界限設定樣本數大小之權衡分析 59
第四章 統計容差界限設定之標準作業流程與數值實例分析 61
第一節 統計容差界限設定之標準作業流程 61
第二節 常態分配下統計容差界限設定之實例 64
第三節 非常態分配下無母數統計容差界限設定之實例 65
第四節 非常態分配下屬於特定分配統計容差界限設定之實例 67
第五章 結論與未來研究方向 70
第一節 結論 70
第二節 未來研究方向 71
參考文獻 72
附錄A 74
附錄B 86

參考文獻 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
1.Bain, L. J. and Engelhardt, M. (1981). “Simple Approximate Distributional Results for Confidence and Tolerance Limits for the Weibull Distribution Based on Maximum Likelihood Estimators,” Technometrics, Vol. 23, No.1, pp. 15-20.
2.Blischke, W. R. and Murthy, D. N. P. (2000). Reliability: Modeling, Prediction, and Optimization, John Wiley & Sons, New York.
3.Ellison, B. E. (1964). “On Two-Sided Tolerance Intervals for a Normal Distribution,” Annals of Mathematical Statistics, Vol. 35, No. 2, pp. 762-772.
4.Faulkenberry, G. D. and Weeks, D. L. (1968). “Sample Size Determination for Tolerance Limits,” Technometrics, Vol. 10, No. 2, pp. 343-348.
5.Hahn, G. J. and Meeker, W. Q. (1991). Statistical Intervals: A Guide for Practitioners, John Wiley & Sons, New York.
6.Howe, W. G. (1969). “Two-Sided Tolerance Limits for Normal Populations, Some Improvements,” Journal of the American Statistical Association, Vol. 64, No. 326, pp. 610-620.
7.Krishnamoorthy, K. and Mathew, T. (2009). Statistical Tolerance Regions: Theory, Applications, and Computation, John Wiley & Sons, Hoboken.
8.Krishnamoorthy, K., Mathew, T. and Mukherjee, S. (2008). “Normal-Based Methods for a Gamma Distribution: Prediction and Tolerance Intervals and Stress-Strength Reliability,” Technometrics, Vol. 50, No. 1, pp. 69-78.
9.Lin, S. S., Wang, B. and Zhang, C. (1997). “Statistical Tolerance Analysis Based on Beta Distributions,” Journal of Manufacturing Systems, Vol. 16, No. 2, pp. 150-158.
10.Montgomery, D. C. (2012). Introduction to statistical quality control, John Wiley & Sons, New York.
11.Owen, D. B. (1964). “Controls of Percentages in Both Tails of the Normal Distribution,” Technometrics, Vol. 6, No. 4, pp. 377-387.
12.Wald, A. (1943). “An Extension of Wilks’ Method for Setting Tolerance Limits,” The Annals of Mathematical Statistics, Vol. 14, No. 1, pp. 45-55.
13.Wald, A. and Wolfowitz, J. (1946). “Tolerance Limits for a Normal Distribution,” Annals of the Mathematical Statistics, Vol. 17, No. 2, pp. 208-215.
14.Weissberg, A. and Beatty, G. (1960). “Tables of Tolerance Limit Factors for Normal Distributions,” Technometrics, Vol. 2, No. 4, pp. 483-500.
15.Wilks, S. S. (1941). “Determination of Sample Sizes for Setting Tolerance Limits,” The Annals of Mathematical Statistics, Vol. 12, No. 1, pp. 91-96.
16.Wilson, E. B. and Hilferty, M. M. (1931). “The Distribution of Chi-Squares,” Proceedings of the National Academy of Sciences, Vol. 17, No. 12, pp. 684-688.
17.Young, D. S. (2010). “tolerance: An R Package for Estimating Tolerance Intervals,” Journal of Statistical Software, Vol. 36, No. 5, pp. 1-39.
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.
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