統計製程管制(SPC)在國際上被公認為可有效提升製程品質的技術，在營造業、工業、製造業等方面均被廣泛應用。品質管制圖是統計製程管制中主要用以監控製程或施工狀況，進而分析過程中的品質特性、製程異常狀況與判定變異原因，進而採用可確保品質穩定改善方案的良好工具。傳統管制圖依數據種類可分為計量值管制圖與計數值管制圖兩類，計量值管制圖技術有X ̅-R(平均數-全距)管制圖、X ̅-S(平均數-變異數)管制圖、中位數管制圖等。計數值管制圖技術有不良率管制圖、缺點數管制圖等。管制圖由管制中心線、管制上限與管制下限組成。管制圖之管制界限係基於樣本的標準差所建立，由樣本落於管制界限的位置判定製程是否處於管制。
然而，在許多情況下，樣本之評量結果可能為語意或模糊數值，導致管制界限無法精確的訂定，而模糊理論被公認是處理當樣本存在不確定性情況的良好工具。利用隸屬函數與模糊運算建立較傳統管制圖更合理與彈性的模糊管制界限。本研究之模糊管制圖，係根據可能性分佈轉換方法，藉由將模糊直方圖轉換為可能性分佈圖形，來判定模糊樣本的分佈情況，並對圖形配適可能性分佈函數，依照其特徵值，制訂管制限制繪製管制圖，最後以案例說明分析結果，方法的有效性以及潛在的應用。
本研究使用針對可能性分佈情形配適之函數建立模糊管制圖模式，係根據可能性理論中的可能性分佈函數，針對計算出的特徵值訂定管制界限，避免過往使用常態分佈近似所有函數產生的誤差。

The statistical process control (SPC) is technique that has been highly recognized internationally and applied throughout construction engineering, industrial and manufacturing. The SPC is a useful to that can be applied to monitor the manufacturing or construction process, then ensure quality stability by identifying special causes and incorrect actions during the process.The traditional control chart can be classified into Variable Control Chart and Attributes Control Chart. Control chart techniques include X ̅–R, X ̅–S and P Control chart is consisted of Center Line, Upper Control Limit and Lower Control Limit. These limits are represented by the numerical values on the basis of the sample average and variance. The process is either “in-control” or “out-of-control” depending on numerical observations.However, under many circumstances, sample assessments could be linguistic or vague data , which cause uncertainty of control limits. In this situation, fuzzy set theory is a useful tool to cope with this uncertainty. Fuzzy control limits are constructed by using membership functions and fuzzy operation can be more flexible and reasonable than the one constructed by traditional control chart. The fuzzy control chart in this research is based on possibility distribution functions transformation method, and identify distribution of fuzzy samples through transfer fuzzy histogram to possibility distribution plot, and fitting the function.then,constructd the control limit and plot the graph. Last, illustrate result, effectiveness for research method and potential applications of case.

英文文獻
Aichouni, M., Al-Ghonamy, A.I. and Bachioua, L., “Control charts for non-normal data: illustrative examples from the construction industry business”, Mathematical and Computational Methods in Science and Engineering, ISBN: 978-960-474-372-8, pp. 71-76, 2014.
AbouRizk, S. and Halpin, D., “Statistical properties of construction duration data”, Journal of Construction Engineering and Management, 118(3), pp.525-44, 1992.
Anjani Kumar, K. V. N. S. and Mohapatra, P. K. J., “A new approach to design of fuzzy Multi-Attribute control charts”, Indian Institute of Technology, 2012.
Amirzadeh, V., Mashinchi, M. and. Yaghoobi, M.A., “Construction of Control Charts Using Fuzzy Multinomial Quality”, Journal of Mathematics and Statistics, 4 (1), pp. 26-31, 2008.
Ben Slimen, Y. Ayachi, R. and Ben Amor, N., “Probability-Possibility transformation : Inference study for min-based possibilistic networks”, rencontres francophones sur la Logique Floue et ses Applications 10-11, (2013)
Clements, John A., “Process capability calculations for non-normal distributions”, Quality Progress, 22, pp. 98-100, 1989.
Chou, C.Y., Li, M.H.C. and Wang, P.H., “Economic statistical design of averages control charts for monitoring a process under non-normality”, The International Journal of Advanced Manufacturing Technology. Vol. 17, pp. 603-609, 2001.
Chua, D. and Goh, Y., “Poisson model of construction incident occurrence”, Journal of Construction Engineering and Management 131, 715–722, 2005.
Cheng, C.B., “Fuzzy process control: Construction of control charts with fuzzy numbers”, Fuzzy Sets and Systems, 154, pp. 287–303, 2005.
Civanlar, M.R. and Trussel, H.J., “Constructing membership functions using statistical data”, Fuzzy Sets and Systems 18, pp. 1–13, 1986.
Duclos, E., Pillet, M. and Avrillon, L., “The L-chart for non-normal process”, Quality Technology of Quantitative Management, 2(1), pp. 77-90, 2005.
Dubois, D. and Prade, H., “On several representations of an uncertain body of evidence”, Fuzzy Information and Decision Process, pp. 167-182, 1982.
Dubois, D. and Prade, H., “Theory and Applications”, Fuzzy Sets and Systems, Academic Press, New York, 1980.
Dubois, D. and Prade, H., “On possibility/probability transformations.”, Fuzzy Logic, 1993.
Delgado, M.and Moral, S., “On the concept of possibility-probability consistency”, Fuzzy Sets and Systems 21, pp. 311–318, 1987.
Dabuxilatu, Wang. and Olgiers, Hryniewicz., “A fuzzy nonparametric Shewhart chart based on the bootstrap approach”, Int. J. Appl. Math. Comput. Sci., Vol. 25, No. 2, 389–401, 2015.
El-Shal, S.M. and Morris, A.S., “A fuzzy rule-based algorithm to improve the performance of statistical process control in quality systems”, Journal of Intelligent and Fuzzy Systems, 9, pp. 207–223, 2000.
Filzmoser, R. and Vertl, R., “Testing hypotheses with fuzzy data: the fuzzy p-value”, Metrika, 59, pp. 21–29, 2004.
Gűlbay, M. and Kahraman, C., “An alternative approach to fuzzy control charts:　Direct fuzzy approach”, Information Sciences, 177, pp.1463–1480, 2007.
Gűlbay, M. and Kahraman, C., “Design of Fuzzy Process Control Charts for Linguistic and Imprecise Data”, Fuzziness and Soft Computing, 201, pp.59-88, 2006.
Grzegorzewski, P. and Hryniewicz, O., “Soft methods in statistical quality control”, Control and Cybernetics 29, pp. 119–140, 2000.
Inuiguchi, M. and Sakawa, M., “Possible and necessary efficiency in possibilistic multi-objective linear programming problems and possible efficiency test,” Fuzzy Sets and Systems, 78, pp. 231-241, 1996.
Klir, G. J. “Probability-possibility transformations: a comparison”, Int J General Systems 21: 291-310, 1992.
Kanagawa, A., Tamaki, F. and Ohta, H., “Control charts for process average and variability based on linguistic data”, International Journal of Production Research, 2, pp. 913–922, 1993.
Kahraman, C., Tolga E. and Ulukan. Z., “Using triangular fuzzy numbers in the tests of control charts for unnatural patterns”, Proceedings of INRIA/IEEE Conference on Emerging Technologies and Factory Automation, October 10–13, Paris–France, vol. 3, pp. 291–298, 1995.
Laviolette, M., Seaman, J.W., Barrett, J.D. and Woodall, W.H., “A probabilistic and statistical view of fuzzy methods, with discussion”, Technometrics, 37, pp. 249–292, 1995.
Lilliefors, H., “On the Kolmogorov–Smirnov test for normality with mean and variance unknown”, Journal of the American Statistical Association, Vol. 62. pp. 399–402, 1967.
Lee, D., Lim, T. and Arditi, D., “Stochastic project financing analysis system for construction”, Journal of Construction Engineering and Management, 138 (3), pp. 376-389, 2012.
Mouchaweh, M. S. Bouguelid, M. S. Billaudel, P. and Riera, B. “Variable probability-possibility transformation”, 25th European Annual Conference on Human Decision-Making and Manual Control, p 417–428, 2006.
Mauris G., “Representing and approximating symmetric and asymmetric probability coverage intervals by possibility distributions”, IEEE Transactions on Instrumentation Measurement, 58(1), pp.41-45, 2009.
Malcolm, D.G., Roseboom, C.E., Clark, C.E. and Fazar, W., “Application of a technique for research and development program evaluation”, Operations Research, Vol.7, pp.646–649, 1959.
Maio, C., Schexnayder, C., Knutson, K. and Weber, S., “Probability distribution functions for construction simulation”, Journal of Construction Engineering and Management, 126(4), pp. 285-292, 2000.
Masson, M-H. and Denoeux, T., “Inferring a possibility distribution from empirical data”, Fuzzy Sets and Systems 157, 319–340, 2006.
Pan, N.-F., “Evaluation of building performance using fuzzy FTA”, Construction Management and Economics, 24 (12), pp. 1241-1252, 2006.
Puri, M.L. and Ralscu, D.A., “Fuzzy random variables”, Journal of Mathematical Analysis and Applications, Vol.114, pp. 409-422, 1986.
Pandurangan, A. and Varadharajan, R., “Construction of α-cut fuzzy X ̅ ̃-R ̃ and X ̅ ̃-S ̃ Control Charts Using Fuzzy Trapezoidal Number”, IJRRAS 9 (1), 2011.
Rodriguez, R. N., “Recent developments in process capability analysis”, JQT Vol. 24 No. 4, 1992.
Rommelfanger, H., “Fuzzy linear programming and applications”, Fuzzy Sets and Systems, 92, pp. 516-527, 1996.
Raz, T. and Wang, J.-H., “Probabilistic and membership approaches in the construction of control charts for linguistic data”, Production Planning and Control, 1, pp.147–157, 1990.
Samanta, B. and Bhattacherjee, A.,”Problem of non-normality in statistical quality control:a case study in a surface mine”, The Journal of The South African Institute of Mining and Metallurgy, pp. 257-264, 2004.
Schexnayder, C., Knutson, K. and Fente, J., “Describing a beta probability distribution function for construction simulation”, Journal of Construction Engineering and Management, 131(2), 221–229, 2005.
Shiraishi, N. and Furuta, H.,”Reliability analysis based on fuzzy probability”, Journal of Engineering Mechanics 109(6), pp. 1445-1459, 1983.
Shewhart, W.A., “Economic control of quality of manufactured product”, D. Van Nostrand, Inc., Princeton, NJ, 1931.
Schilling, E.G. and Nelson, P.R., “The effect of non-normality on the control limit of X ̅ charts”, Journal of Quality Technology, 8, pp. 183-187, 1976.
Touran, A. and Wiser, E., “Monte Carlo technique with correlated random variables.” Journal of Construction Engineering and Management, ASCE, Vol.118, No.2, pp. 258-272, 1992.
Tannock, J.D.T., “A fuzzy control charting method for individuals”, International Journal of Production Research, 41(5), pp.1017-1032, 2003.
Viertl, R. and Hareter, D., “Fuzzy estimation and imprecise probability”, Journal of Applied Mathematics and Mechanics, 84(10-11), pp. 731–739, 2004.
Veljkovic, K., Elfaghihe, H. and Jevremovic, V., “Economic statistical design of X bar control chart for non-normal symmetric distribution of quality characteristic”, Filomat, 29(1), pp. 2325-2338, 2015.
Wang, J.-H. and Raz, T., “Applying fuzzy set theory in the development of quality control charts”, International Industrial Engineering Conference Proceedings, Orlando, FL, pp. 30–35, 1988.
William, T.M., “Practical use of distributions in network analysis”, Journal of the Operational Society, 43/3, pp. 265-270, 1962.
Wonneberge, S., “Generalization of an invertible mapping between probability and possibility”, Fuzzy Sets and Systems 64 (2), pp. 229–240, 1994.
Zadeh, L.A., “Fuzzy sets”, Information and control,” vol.8, pp. 338-353, 1965.
Zadeh, L. A., “Fuzzy sets as a basis for a theory of possibility”, Fuzzy Sets and Systems, 1, pp. 3-28, 1978.
中文文獻
1. 王維志與李建中，「電腦模擬與單價比對在工程採購招標之運用」，中國土木水利工程學會會刊，第二十七卷，第四期，第 3-12 頁，2001。
2. 吉琳娜，「可能性分佈合成理論及其工程應用研究」，博士論文，中北大學信號與信息處理研究所，2011
3. 邱思瑀，「以生命週期衝擊評估作為環境影響評估之分析工具及其不確定性分析」，碩士論文，明志科技大學環境與資源工程研究所，2011。
4. 侯世旺與同淑蓉，「基於模糊數的模糊過程品質管制圖研究」，鄭州大學，2008。
5. 莊月璇，「台灣地區風速機率分佈之研究」，碩士論文，國立中央大學土木工程研究所，2001。
6. 張景鐘，「台灣風力載重規範中相關係數之可靠度研究」，國科會專題研究報告，1995。
7. 曾郁婷，「小樣本的常態性檢定之探討」，碩士論文，真理大學數理科學研究所碩士班，2008。
8. 鄒家昇，「速食餐飲人力與資源配置之模擬研究」，國立國防大學，碩士論文(2005)。
9. 潘南飛，「工程品質查檢知識庫之建構」，營建知識管理研討會，高雄，2003。
10. 蔡堯波，「需求隨價格變動的報童模式之探討--以模糊理論可能性分配取代機率分配」，國立臺灣科技大學管理技術研究所，1993。
11. 蔡瑞舫、張憲國、劉勁成、曾相茂，「臺灣離岸與陸岸風速分步特性之探討」，第35屆海洋工程研討會論文集，2013。
12. 謝幼屏，「提升高雄港貨櫃碼頭營運效益之研究」，96-72-7286 MOTC-IOT-95-H1DA004-1，交通部運輸研究所，2007。
13. 謝名起，「利用可能性分配在成本數量利潤分析之研究」，碩士論文，國立成功大學工業管理研究所，2000。