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系統識別號 U0026-0812200911515243
論文名稱(中文) 模糊資料之製程能力指標
論文名稱(英文) Process Capability Indices with Fuzzy Numbers
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 94
學期 2
出版年 95
研究生(中文) 楊惠萍
研究生(英文) Hwei-Ping Yang
學號 r2693407
學位類別 碩士
語文別 英文
論文頁數 55頁
口試委員 指導教授-呂金河
指導教授-許秀麗
口試委員-潘浙楠
中文關鍵字 模糊隸屬函數  製程能力指標  模糊集合  模糊數 
英文關鍵字 fuzzy set  membership function  Process capability indices  fuzzy numbers 
學科別分類
中文摘要 製程能力指標是品質管制上用來量測製程能力之最常用的方法,在理論上與實務上都有許多重要的研究成果。傳統的製程能力指標是用明確的觀察數值來建構的,但是觀察值的量測不可能完全無誤差。這裡的誤差是指非抽樣誤差,在統計理論上是無法避免的。因此我們把觀察值視為不確定的模糊數,利用模糊理論來討論模糊製程能力指標。
當認定觀察值不是精確的數值時,本論文利用模糊數來替代明確數值,透過模糊數學運算,來建構模糊化的製程能力指標。建構出模糊製程能力指標後,我們探討模糊製程能力指標對應的模糊不良率及其相關的模糊統計推論。
模糊化的製程能力指標,是對整體製程表現之評估。明確值的傳統製程能力指標,是本研究模糊化的製程能力指標之特別情形。

英文摘要 Process capability indices (PCIs) are the most commonly used method to measure process capability in quality control. There are many important research efforts whether in the theory or in practice. Traditionally, PCIs are constructed with observations which are crisp numbers. But the error exists during observational process. Statistics cannot avoid the non-sampling error. Therefore the fuzzy set theory is introduced into our study to construct PCIs, when data are non-precise.
While observations are regarded as imprecision, clear-cut numbers are replaced by fuzzy numbers through operation on the fuzzy set to compute fuzzy process capability indices, then we discussion the fuzzy percentage of non-conforming and fuzzy statistical inference for fuzzy PCIs.
Fuzzy process capability indices can also display the performance of process capability. Thus, traditional crisp process capability indices are a special case for fuzzy process capability indices.

論文目次 Chapter 1 Introduction 1
1.1 Two Basic Capability Indices: Cp and Cpk 1
1.2 The Fuzzy Set Theory and Fuzzy Operation 3
1. 2. 1 The Fuzzy Sets versus Crisp Sets 3
1. 2. 2 α-cuts, Decomposition Principle and Extension Principle 6
1. 2. 3 Operations on the Fuzzy Sets 7
1. 2. 4 Fuzzy Random Variable 8
1.3 Overview 9
Chapter 2 Literature Review 10
Chapter 3 Fuzzy and Fuzzy 14
3.1 Fuzzy Standard Deviation 14
3.2 Fuzzy Data and Fuzzy Bounds of Specifications 18
3.2.1 Estimation of Fuzzy Cp 19
3.2.2 Estimation of Fuzzy Cpk 21
3.3 Fuzzy Data and the Crisp Specification 22
3.3.1 Estimation of fuzzy Cp* 22
3.3.2 Estimation of fuzzy Cpk* 23
3.4 The Fuzzy Percentage of Non-conforming 24
3.4.1 The Percentage Non-conforming of Cp and Cpk 24
3.4.2 The Relationship of Index Cp and the Percentage of Non-conforming of 26
3.5 Statistical Inference 29
3.5.1 Confidence Interval for Cp 29
3.5.2 Confidence Interval for Cpk 32
3.5.3 Hypothesis Testing with Cp and Cpk 34
Chapter 4 Data Analysis 37
Chapter 5 Concluding Remarks 46
References 47
Appendix 48
參考文獻 1. Cen, Y. (1996), “Fuzzy quality and analysis on fuzzy probability,” Fuzzy sets and systems, 83, 283-290.
2. Tsai C. C. and Chen C. C. (2005), “Making decision to evaluate process capability index with fuzzy numbers,” International Journal of Advanced Manufacturing technology, DOI. 10.1007/s00170-005-0052-7.
3. Grzegorzewski, P. (2000), “Testing statistical hypotheses with vague data,” Fuzzy sets and systems, 112, 501-510.
4. Hong, D. H. (2004), “A note on index estimation using fuzzy numbers,” European Journal of Operational Research, 158, 529-532.
5. Kaufmann, A. and Gupta M. M. (1988), Fuzzy mathematical models in engineering and management science. North-Holland, New York.
6. Kotz, S. and Lovelance, C. R. (1998), Process capability indices in theory and practice. Arnold, New York.
7. Kruse, R. and Meyer, K.D. (1987), Statistics with vague data. D. Reidel Publ., Dordretch.
8. Kwakernaak, H. (1978), “Fuzzy random variables,” Information Science, 15, 1-15.
9. Lee, H. T. (2001), “ index estimation using fuzzy numbers,” European Journal of Operational Research, 129, 683-688.
10. Viertl, R. (1996), Statistical methods for non-precise data. Fla.: CRC Press, Boca Raton.
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