臺灣博碩士論文加值系統

在製程中有時觀察值不能精確的量測，我們將之視為不確定的模糊數。對於模糊資料，本研究藉由模糊理論的兩大定理：分解定理及擴展定理，分別建構 - 管制圖，用以監控製程品質特性中的平均數與標準差，再使用模糊排序方法比較模糊數，判斷製程處於“管制狀態”、“失控狀態”、“相當於管制狀態”、“相當於失控狀態”下，比起傳統管制圖提供更多資訊以利於決策者決策。最後舉一個以車削方式製造光學鏡片之表面粗糙度例子，說明如何使用 - 管制圖監控模糊資料。

Traditionally, variable control charts are constructed based on precise data collected from well-defined quality characteristics of manufacturing products. However, in the real world there are many occasions the stated quality characteristic of products such as surface roughness of optical lens or light transmittance of touch screens contains somewhat degree of imprecise information so that their readings inevitably gather as fuzzy numbers (data). In this situation, the traditional method for constructing the variable control charts exists a limitation of dealing with fuzzy data when the average and variance of underlying quality characteristic are monitored. Therefore, in this paper we propose and control charts with fuzzy data, whose fuzzy control limits are obtained on the basis of employing two well-known principles, so called resolution identity and extension principle, in the fuzzy theory. Furthermore, for comparing fuzzy observations and fuzzy control limits, a fuzzy ranking method is presented to classify the underlying manufacturing process condition. Finally, a practical example is provided to demonstrate the applicability of our proposed methodologies.

Chinese Abstract i
English Abstract ii
Acknowledgements iii
Contents iv
List of Table vi
List of Figure vii
1. Introduction 1
1.1 Control Charts for Real-Valued Data 4
1.2 The Fuzzy Set Theory and Fuzzy Operation 6
1.2.1 Fuzzy Numbers 6
1.2.2 Fuzzy Operation 8
1.2.3 Resolution Identity 8
1.2.4 Extension Principle 9
1.3 Overview 10
2. Review on Fuzzy Control Chart 11
3. Proposed Method 16
3.1 Fuzzy and Control Charts for Fuzzy Data by Resolution Identity 16
3.2 Fuzzy and Control Charts for Fuzzy Data by Extension Principle 20
3.3 Methods for Classifying the Manufacturing Process 25
4. Practical Analysis 27
4.1 Practical Example 27
4.2 Step-by-Step Analysis Procedure 33
4.2.1 Fuzzy and Control Chart with Resolution Identity 36
4.2.2 Fuzzy and Control Chart with Extension Principle 41
4.3 The Comparison with the Traditional and Control Chart 46
5. Concluding Remarks 49
References 50

[1]Devor RE, Chang T, Sutherland JW, 1992, Statistical Quality Design and Control: contemporary concepts and methods, Macmillan, New York.
[2]Douglas C. Montgomery, 2008, Introduction to Statistical Quality Control, 6th Edition, Arizona State University.
[3]V. Amirzadeh, M. Mashinchi, M.A. Yaghoobi, 2008, “Construction of Control Charts Using Fuzzy Multinomial Quality”, Journal of Mathematics and Statistics, vol. 4, no. 1, pp.26-31.
[4]M. Gülbay, C. Kahraman, D. Ruan, 2004, “α-Cut Fuzzy Control Charts for Linguistic Data”, International Journal of Intelligent Systems, pp.1173-1196.
[5]Hsien-Chung Wu, 2003, “Linear Regression Analysis for Fuzzy Input and Output Data Using the Extension Principle”, Computers and Mathematics with Applications, vol. 45, pp.1849-1859.
[6]L.A. Zadeh, 1965, “Fuzzy sets”, Information and Control, vol. 8, pp.338-353.
[7]Marcucci M., 1985, “Monitoring multinomial processes”, Journal of Quality Technology, vol. 17, pp.86-91.
[8]J.-H. Wang, T. Raz, 1990, “On the construction of control charts using linguistic variables”, International Journal of Production Research, vol. 28, pp.477-487.
[9]T. Raz, and J.-H. Wang, 1990, “Probabilistic and membership approaches in the construction of control charts for linguistic data”, Production Planning and Control, vol. 1, pp.147-157.
[10]A. Kanagawa, F. Tamaki, H. Ohta, 1991, “Fuzzy control charts for linguistic data”, IFES’, vol. 91, pp.644–654.
[11]L.A. Zadeh, 1968, “Probability measure of fuzzy events”, J. Math. Anal. Appl, vol. 28, pp.421–427.
[12]Shendy M. El-Shal and Alan S. Morris, 2000, “A fuzzy rule-based algorithm to improve the performance of statistical process control in quality systems”, Journal of Intelligent and Fuzzy Systems, vol. 9, pp.207-223.
[13]Taleb, H. and M. Limam, 2002, “On fuzzy and probabilistic control charts” International Journal of Production Research, vol. 40, pp.2849-2863.
[14]Cheng, C.B., 2003, “Fuzzy process control based on fuzzy regression and possibility measures”, IEEE, pp.127-131.
[15]Cheng, C.B., 2005, “Fuzzy process control: Construction of control charts with fuzzy numbers”, Fuzzy Sets and Systems, vol. 154, pp.287-303.
[16]M. Gülbay, C. Kahraman, 2007, “An alternative approach to fuzzy control charts: Direct fuzzy approach”, Information Sciences, vol. 177, pp.1463-1480.
[17]Faraz, A. and M. Bameni Moghadam, 2007, “Fuzzy control chart a better alternative for Shewhart average chart”, Quality and Quantity, vol. 41, pp.375-385.
[18]Ming-Hung Shu and Hsien-ChungWu, 2010, “Monitoring imprecise fraction of nonconforming items using p control charts”, Journal of Applied Statistics, vol. 37, no. 8, pp.1283–1297.
[19]Ming-Hung Shu and Hsien-ChungWu, 2011, “Fuzzy and R Control Charts: Fuzzy Dominance Approach”, Computers & Industrial Engineering, vol.x, pp.xxx.
[20]Yuan, Y. 1991. “Criteria for evaluation fuzzy ranking methods”. Fuzzy Set and Systems, vol. 43, pp.139-157.
[21]D. Dubois, H. Prade, 1978, “Operations on fuzzy numbers”, Int. J. Systems Sci, vol. 9, pp.613-626.
[22]D Dubois, H Prade, 1980, Fuzzy sets and Systems: Theory and Application, Academic Press, New York.
[23]Zadeh, L.A., 1975, “The concept of linguistic variable and its application to approximate reasoning I”, Inform. Sci., vol.8, pp.199-249.
[24]Zadeh, L.A., 1975, “The concept of linguistic variable and its application to approximate reasoning II”, Inform. Sci., vol.8, pp.301-357.
[25]Zadeh, L.A., 1975, “The concept of linguistic variable and its application to approximate reasoning III”, Inform. Sci., vol.9, pp.43-80.
[26]M.S. Bazarra and C.M. Shetty, 1993, Nonlinear Programming, Wiley, New York.
[27]W. Rudin, 1986, Real and Complex Analysis, Third Edition, McGraw-Hill.
[28]E. Paul Degarmo J, T. Black Ronald A, Kohser, 1997, Materials and processes in manufacturing, pp.288-290.
[29]Dr. Mike S. Lou, Dr. Joseph C. Chen, Dr. Caleb M. Li, 1999, “Surface roughness prediction technique for CNC end milling”, Journal of industrial technology, vol. 15, pp.1-6.
[30]Thomas, T.R., 1999, Rough Surfaces, 2nd ed., Imperial College Press, London.
[31]Mummery L, 1990, Surface Texture Analysis-The Handbook. Hommelwerke Gmbh, Germany.