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研究生:張傑生
研究生(外文):JYE-SHENG CHANG
論文名稱:基於非對稱允差規格製程之計量型驗收抽樣計畫設計
論文名稱(外文):Design of Variables Acceptance Sampling Plans for Products with Asymmetric Tolerances
指導教授:吳建瑋吳建瑋引用關係
指導教授(外文):Chien-Wei Wu
口試委員:吳建瑋
口試日期:2012-05-23
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:工業管理系
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:109
中文關鍵詞:製程能力分析非對稱允差規格驗收抽樣計畫決策判斷
外文關鍵詞:Process capability analysisAsymmetric toleranceAcceptance sampling planDecision making
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驗收抽樣計畫(Acceptance Sampling Plan)是一項在品質管理和品質保證領域中非常典型且實用的工具。它能夠協助買賣雙方對交貨產品是否滿足指定品質要求做出貨批判定的決策。然而隨著科技的進步,製程技術與品質不斷的提升,製程所產出的不良品已相當低,傳統計數型的驗收抽樣計畫,在抽檢合理的樣本下,幾乎都沒有不良品出現,因此有可能無法反應出貨批的實際情況而造成誤判及損失。而製程能力指標(Process Capability Indices, PCIs)提供製程一個量化的數據來衡量其產出的績效水準,即使在非常高良率的製程水準,仍能有效使用,因此製程能力指標已是品質管制上相當重要的工具。然而,過去的製程能力分析大多是針對製造規格區間為對稱型(Symmetric)下做探討,而當製程為非對稱型態(Asymmetric)時,則可能造成誤判而無法使用。因此本研究主要擬針對非對稱區間規格下,基於製程能力指標 來設計兩種計量型的驗收抽樣計畫,亦即單次驗收抽計畫(Variables Single Sampling Plan, VSSP)與計量型重覆群集收樣計畫(Variables Repetitive Group Sampling Plan, VRGS)。為了便於使用,針對在不同風險水準及常見的品質要求下,將檢驗所需抽樣樣本數和臨界值整理成表格,並提供逐步操作程序。最後輔以實例做為分析與說明,以供日後參考使用。
Acceptance sampling plan is a classical and very useful tool for quality management and quality assurance. It can help vendors and buyers make decisions on whether the products meet the quality requirement. As the advancement manufacturing technology, the process capability is quite high with very low fraction of defectives. Under this situation, any reasonable sample size probably contains no defective product. Therefore, traditional attributes acceptance sampling plan cannot work. Existing works on process capability analysis have focused on developing and investigating PCIs for cases with symmetric tolerances, but not for case with asymmetric tolerances. In this thesis, we develop two variables acceptance sampling plans, VSSP and VRGSP, based on the index to deal with product acceptance determination for cases with asymmetric tolerances. For users’ convenience, table of the sample size required for inspection and critical value under various quality levels and risks and a step-by-step procedure are provided. Finally, application examples are given for illustration.
中文摘要………………………………………………………………………………i
英文摘要……………………………………………………………………………ii
致 謝……………………………………………………………………………iii
圖目錄………………………………………………………………………………vi
表目錄………………………………………………………………………………viii
第一章 緒論…………………………………………………………………………1
1.1 研究背景與動機………………………………………………………1
1.2 研究目的………………………………………………………………2
1.3 研究架構………………………………………………………………2
第二章 文獻探討……………………………………………………………………5
2.1 製程能力指標…………………………………………………………5
2.2 非對稱製程能力指標…………………………………………………7
2.3 非對稱製程能力指標 ………………………………………………9
2.3.1 指標的估計式………………………………………………9
2.3.2 指標的抽樣分配…………………………………………10
2.4 驗收抽樣計畫介紹及其相關文獻回顧………………………………11
2.4.1驗收抽樣計畫介紹………………………………………………11
2.4.2驗收抽樣計畫相關文獻回顧……………………………………12
第三章 單次抽樣計畫………………………………………………………………14
3.1 以製程能力指標 來設計單次驗收抽樣計畫……………………14
3.2 分配特徵參數 ………………………………………………………16
3.3 求解聯立方程式……………………………………………………21
3.4 抽樣計畫程序以及判斷準則…………………………………………26
3.5 實例分析……………………………………………………………27
3.6 結論……………………………………………………………………31
第四章 重覆群集抽樣計畫…………………………………………………………33
4.1 以製程能力指標 來設計重覆群集抽樣計畫……………………33
4.2求解方程式……………………………………………………………39
4.3抽樣計畫程序以及判斷準則…………………………………………44
4.4 實例分析………………………………………………………………44
4.5 結論……………………………………………………………………48
第五章 分析與比較………………………………………………………………49
5.1 檢驗樣本數…………………………………………………………49
5.2 操作特性曲線………………………………………………………51
5.3 結論……………………………………………………………………53
第六章 結論與未來研究方向………………………………………………………54
參考文獻……………………………………………………………………………56
附錄…………………………………………………………………………………59
一、中文部分
1.蘇朝墩 (2010),「品質管理」,前程文化事業有限公司。
2.智訓有限公司,http://www.wdtc.com.tw/index.php。
二、英文部分
1.Balamurali, S. and Jun, C. H. (2006). Designing of a variables two- plan system by minimizing the average sample number. Journal of Applied Statistics, 36(10), 1159-1172.
2.Bender, A. J. (1975). Sampling by variables to control the fraction defective: part II. Journal of Quality Technology, 7, 139-143.
3.Boyles, R. A. (1991). The Taguchi capability index. Journal of Quality Technology, 23(1), 17-26.
4.Das, N. G. and Mitra, S. K. (1964). The effect of non-normality on sampling inspection by variables. Sankhya: The Indian Journal of Statistics, 26, 169-176.
5.Franklin, L. A. and Wasserman, G. (1992). Bootsrtap lower confidence limits for capability indices, Journal of Quality Technology, 24, 196-210.
6.Govindaraju, K. and Soundararajan, V. (1986). Selection of single sampling plans for variables matching the MIL-STD-105 scheme. Journal of Quality Technology, 18(4), 234-238.
7.Hailey, W. A. (1980). Minimum sample size single sampling plans: a computerized approach. Journal of Quality Technology, 12(4), 230-235.
8.Jennett, W. J. and Welch, B. L. (1939). The control of proportion defective as judged by a single quality characteristic varying on a continuous scale. Journal of Royal Statistical Society, Series B, 6(1), 80-88.
9.Juran, J. M. (1974). Quality Control Handbook, 3rd ed., McGraw-Hill, New Work, USA.

10.Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18, 41-52.
11.Kushler, R. H. and Hurlry, P. (1992). Confidence bounds for capability indices, Journal of Quality Technology, 24, 188-195.
12.Lieberman, G. J. and Resnikoff, G. J. (1955). Sampling plans for inspection by variables. Journal of the American Statistical Association, 50, 475-516.
13.Montgomery, D. C. (2004). Introduction to Statistical Quality Control, 5th ed., New York, Wiley.
14.Nergin, I., Parmet, Y. and Schechtman, E. (2011). Developing a sampling plan based on Cpk–unknown variance. Quality and Reliability Engineering International, 27, 3-14.
15.Owen, D. B. (1967). Variables sampling plans based on the normal distribution. Technometrics, 9(3), 417-423.
16.Pearn, W. L. and Chen, K. S. (1997). Multiprocess performance analysis: a case study. Quality Engineering, 10(1), 1-8.
17.Pearn, W. L. and Chen, K. S. (1998). New generalization of process capability index Cpk. Journal of Applied Statistics, 25, 801-810.
18.Pearn, W. L., Lin, P. C. and Chen, K. S. (2004). The index for asymmetric tolerances: Implications and inference. Metrika – International Journal for Theoretical and Applied Statistics, 60, 119-136
19.Pearn, W. L. and Wu, C. W. (2006a). Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives. Omega – The International Journal of Management Science, 34(1), 90-101.
20.Pearn, W. L. and Wu, C. W. (2006b). Variables sampling plans with PPM fraction of defectives and process loss consideration. Journal of the Operational Research Society, 57(4), 450-459.

21.Pearn, W. L. and Wu, C. W. (2007). An effective decision making method for product acceptance. Omega – The International Journal of Management Science, 35(1), 12-21.
22.Sherman, R. E. (1965). Design and evaluation of repetitive group sampling plan. Technometrics, 7, 11-21
23.Suresh, R. P. and Ramanathan, T. V. (1979). Acceptance sampling plans by variables for a class symmetric distributions. Communications in Statistics: Simulation and Computation, 26(4), 1379-1391.
24.Wu, C. W., Aslam, M., Chen, J. C. and Jun, C. H. (2011) A Variables repetitive group sampling plan for lot sentencing based on process performance index. Working Paper, National Taiwan University of Science and Technology, Taiwan.
25.Wu, C. W., Aslam, M. and Jun, C. H. (2012). Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk. European Journal of Operational Research, 217, 560-566.
26.Wu, C. W. and Pearn, W. L. (2008). A variables sampling plan based on for product acceptance determination. European Journal of Operational Research, 184(2), 549-560.
27.Yen, C. H. and Chang, C. H. (2009). Designing variables sampling plan with process loss consideration. Communications in Statistics: Simulation and Computation, 38, 1579-1591.
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