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題名 最大利潤下規格上限與EWMA管制圖之設計
Design of upper specification and EWMA control chart with maximal profit作者 蔡佳宏
Tsai, Chia Hung貢獻者 楊素芬
蔡佳宏
Tsai, Chia Hung關鍵詞 Economic design
Specification
EWMA control chart
VSI control chart
Markov chain
Gamma distribution
Optimization technique日期 2011 上傳時間 30-Oct-2012 10:13:35 (UTC+8) 摘要 The determination of economic control charts and the determination of specification limits with minimum cost are two different research topics. In this study, we first combine the design of economic control charts and the determination of specification limits to maximize the expected profit per unit time for the smaller the better quality variable following the gamma distribution. Because of the asymmetric distribution, we design the EWMA control chart with asymmetric control limits. We simultaneously determine the economic EWMA control chart and upper specification limit with maximum expected profit per unit time. Then, extend the approach to determine the economic variable sampling interval EWMA control chart and upper specification limit with maximum expected profit per unit time.In all our numerical examples of the two profit models, the optimum expected profit per unit time under inspection is higher than that of no inspection. The detection ability of the EWMA chart with an appropriate weight is always better than the X-bar probability chart. The detection ability of the VSI EWMA chart is also superior to that of the fixed sampling interval EWMA chart. Sensitivity analyses are provided to determine the significant parameters for the optimal design parameters and the optimal expected profit per unit time. 參考文獻 [1] Ardia, D., Mullen, K., Peterson, BG. and Ulrich, J. (2011), DEoptim, Differential Evolution Optimization in R. URL http://CRAN.R-project.org/package=DEoptim.[2] Bai, D. S. and Lee, K. T. (1998), “An economic design of variable sampling interval control charts,” International Journal of Production Economics, 54, 57-64.[3] Cho, B. R. and Phillips, M. D. (1998a), “Design of the optimum product specifications for S-type quality characteristics,” International Journal of Production Research, 36(2), 459-474.[4] Cho, B. R. and Phillips, M. D. (1998b), “An Empirical Approach to Designing Product Specifications: A Case Study,” Quality Engineering, 11(1), 91-100.[5] Chou, C. Y., Chen, C. H. and Liu, H. R. (2006), “Economic Design of EWMA Charts with Variable Sampling Intervals,” Quality & Quantity, 40, 879–896.[6] Crowder, S. V. (1987), “A simple method for studying run length distributions of exponentially weight moving average control charts,” Technometrics, 29, 401–407.[7] Duncan, A. J. (1956), “The economic design of charts used to maintain current control of a process,” Journal of the American Statistical Association, 51(274), 228–242.[8] Feng, Q. and Kapur, K. C. (2006), “Economic development of specifications for 100% inspection based on asymmetric quality loss function,” IIE Transactions, 38, 659-669.[9] Hong, S. H. and Cho, B. R. (2007), “Joint optimization of process target mean and tolerance limits with measurement errors under multi-decision alternatives,” European Journal of Operational Research, 183, 327–335.[10] Hong, S. H., Kwon, H. M., Lee, M. K. and Cho, B. R. (2006), “Joint optimization in process target and tolerance limit for L-type quality characteristics,” International Journal of Production Research, 44(15), 1051-3060.[11] Kapur, K. C. (1988), “An approach for development of specifications for quality improvement,” Quality Engineering, 1(1), 63-77.[12] Montgomery, D. C. (1980), “The economic design of control charts: a review and literature survey,” Journal of Quality Technology, 12(2), 75–87.[13] Montgomery, D. C., Torng, J. C.-C., Cochran J. K. and Lawrence, F. P. (1995), “Statistically constrained economic design of the EWMA control chart,” Journal of Quality Technology, 27(3), 250–256.[14] Panagos, M. R., Heikes R. G. and Montgomery, D. C. (1985), “Economic design of control charts for two manufacturing process models,” Naval Research Logistics Quarterly, 32, 631-646.[15] Plackett, R. L. and Burman, J. P. (1946), “The Design of Optimum Multifactorial Experiments,” Biometrika, 33(4), 305-325.[16] R Development Core Team (2011), R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.[17] Reynolds, M. R. JR., Amin, R. W., Arnold, J. C. and Nachlas, J. A (1988), “ charts with variable sampling intervals,” Technometrics, 30(2), 181-192.[18] Roberts, S. W. (1959), “Control chart tests based on geometric moving averages,” Technometrics, 1, 239-250.[19] Saccucci, M. S. and Lucas, J. M. (1990), “Average run length for exponentially weighted moving average control schemes using the markov chain approach,” Journal of Quality Technology, 22, 154-162.[20] Yang, S. F., Cheng, T. C., Hung, Y. C. and Cheng, S. W. (2012), “A New Chart for Monitoring Service Process Mean,” Quality and Reliability Engineering International, 28(4), 377-386 描述 碩士
國立政治大學
統計研究所
99354011
100資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099354011 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.author (Authors) 蔡佳宏 zh_TW dc.contributor.author (Authors) Tsai, Chia Hung en_US dc.creator (作者) 蔡佳宏 zh_TW dc.creator (作者) Tsai, Chia Hung en_US dc.date (日期) 2011 en_US dc.date.accessioned 30-Oct-2012 10:13:35 (UTC+8) - dc.date.available 30-Oct-2012 10:13:35 (UTC+8) - dc.date.issued (上傳時間) 30-Oct-2012 10:13:35 (UTC+8) - dc.identifier (Other Identifiers) G0099354011 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54172 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 99354011 zh_TW dc.description (描述) 100 zh_TW dc.description.abstract (摘要) The determination of economic control charts and the determination of specification limits with minimum cost are two different research topics. In this study, we first combine the design of economic control charts and the determination of specification limits to maximize the expected profit per unit time for the smaller the better quality variable following the gamma distribution. Because of the asymmetric distribution, we design the EWMA control chart with asymmetric control limits. We simultaneously determine the economic EWMA control chart and upper specification limit with maximum expected profit per unit time. Then, extend the approach to determine the economic variable sampling interval EWMA control chart and upper specification limit with maximum expected profit per unit time.In all our numerical examples of the two profit models, the optimum expected profit per unit time under inspection is higher than that of no inspection. The detection ability of the EWMA chart with an appropriate weight is always better than the X-bar probability chart. The detection ability of the VSI EWMA chart is also superior to that of the fixed sampling interval EWMA chart. Sensitivity analyses are provided to determine the significant parameters for the optimal design parameters and the optimal expected profit per unit time. en_US dc.description.tableofcontents CHAPTER 1. INTRODUCTION 11.1 Research Motivation 11.2 Literature Review 11.3 Research Method 3CHAPTER 2. THE SMALLER THE BETTER QUALITY VARIABLE WITH GAMMA DISTRIBUTION 42.1 In-control Sampling Distribution of X-bar under Gamma Distribution 42.2 Out-of-control Sampling Distribution of X-bar under Gamma Distribution 42.3 Construction of the EWMAX-bar Control Chart Based on X-bar Sampling Distribution 52.4 Calculation of Average Run Length for the EWMAX-bar Chart 62.5 Determining Control Limit Coefficient on EWMAX-bar Control Chart under Different n and λ 72.6 Determining the Best λ in the EWMAX-bar Chart under Different δ1, δ2 and n 11CHAPTER 3. DERIVATION OF THE PROFIT MODEL WITHOUT PRODUCER INSPECTION 193.1 Derivation of Expected Cycle Time 193.2 Derivation of the Expected Cycle Profit 203.3 Determining Optimum Design Parameters of the Economic EWMAX-bar Control Chart 213.4 An Example 223.5 Sensitivity Analysis and Comparing the Results with λ=1 23CHAPTER 4. DERIVATION OF THE PROFIT MODEL WITH PRODUCER INSPECTION 284.1 Derivation of the Expected Cycle Time 284.2 Derivation of the Expected Cycle Profit 284.3 Determining the Optimum Producer Inspection and Design Parameter of the Economic EWMAX-bar Control Chart 294.4 Example and Optimum Results Comparison for with and without Producer Inspection 304.5 Sensitivity Analysis and Comparing the Results of EWMAX-bar Chart with λ=1 32CHAPTER 5. DETERMINING THE BEST λ OF THE ECONOMIC EWMAX-bar CONTROL CHART UNDER DIFFERENT SHIFT SCALES IN THE MEAN AND VARIANCE 375.1 Data Description and Determining the Optimum Producer Inspection and the Design Parameters of the Economic EWMAX-bar Control Chart 375.2 Performance Comparison of Six Numerical Examples 63CHAPTER 6. DETERMINING THE OPTIMUM PRODUCER INSPECTION AND THE ECONOMIC VSI EWMAX-bar CONTROL CHART 656.1 VSI EWMAX-bar Control Chart and ATS Calculation 656.2 Derivation of the Profit Model without Producer Inspection 676.3 Derivation of the Profit Model with Producer Inspection 676.4 Determining Optimum Parameters of the Economic VSI EWMAX-bar Control Chart with and without producer tolerance 686.5 Two Numerical Examples and the Results Comparison with the FSI EWMAX-bar Control Chart 696.6 Sensitivity Analysis and the Optimum Results Comparison between the FSI EWMAX-bar Chart and VSI EWMAX-bar Chart 80CHAPTER 7. SUMMARY 84REFERENCES 86 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099354011 en_US dc.subject (關鍵詞) Economic design en_US dc.subject (關鍵詞) Specification en_US dc.subject (關鍵詞) EWMA control chart en_US dc.subject (關鍵詞) VSI control chart en_US dc.subject (關鍵詞) Markov chain en_US dc.subject (關鍵詞) Gamma distribution en_US dc.subject (關鍵詞) Optimization technique en_US dc.title (題名) 最大利潤下規格上限與EWMA管制圖之設計 zh_TW dc.title (題名) Design of upper specification and EWMA control chart with maximal profit en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1] Ardia, D., Mullen, K., Peterson, BG. and Ulrich, J. (2011), DEoptim, Differential Evolution Optimization in R. URL http://CRAN.R-project.org/package=DEoptim.[2] Bai, D. S. and Lee, K. T. (1998), “An economic design of variable sampling interval control charts,” International Journal of Production Economics, 54, 57-64.[3] Cho, B. R. and Phillips, M. D. (1998a), “Design of the optimum product specifications for S-type quality characteristics,” International Journal of Production Research, 36(2), 459-474.[4] Cho, B. R. and Phillips, M. D. (1998b), “An Empirical Approach to Designing Product Specifications: A Case Study,” Quality Engineering, 11(1), 91-100.[5] Chou, C. Y., Chen, C. H. and Liu, H. R. (2006), “Economic Design of EWMA Charts with Variable Sampling Intervals,” Quality & Quantity, 40, 879–896.[6] Crowder, S. V. (1987), “A simple method for studying run length distributions of exponentially weight moving average control charts,” Technometrics, 29, 401–407.[7] Duncan, A. J. (1956), “The economic design of charts used to maintain current control of a process,” Journal of the American Statistical Association, 51(274), 228–242.[8] Feng, Q. and Kapur, K. C. (2006), “Economic development of specifications for 100% inspection based on asymmetric quality loss function,” IIE Transactions, 38, 659-669.[9] Hong, S. H. and Cho, B. R. (2007), “Joint optimization of process target mean and tolerance limits with measurement errors under multi-decision alternatives,” European Journal of Operational Research, 183, 327–335.[10] Hong, S. H., Kwon, H. M., Lee, M. K. and Cho, B. R. (2006), “Joint optimization in process target and tolerance limit for L-type quality characteristics,” International Journal of Production Research, 44(15), 1051-3060.[11] Kapur, K. C. (1988), “An approach for development of specifications for quality improvement,” Quality Engineering, 1(1), 63-77.[12] Montgomery, D. C. (1980), “The economic design of control charts: a review and literature survey,” Journal of Quality Technology, 12(2), 75–87.[13] Montgomery, D. C., Torng, J. C.-C., Cochran J. K. and Lawrence, F. P. (1995), “Statistically constrained economic design of the EWMA control chart,” Journal of Quality Technology, 27(3), 250–256.[14] Panagos, M. R., Heikes R. G. and Montgomery, D. C. (1985), “Economic design of control charts for two manufacturing process models,” Naval Research Logistics Quarterly, 32, 631-646.[15] Plackett, R. L. and Burman, J. P. (1946), “The Design of Optimum Multifactorial Experiments,” Biometrika, 33(4), 305-325.[16] R Development Core Team (2011), R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.[17] Reynolds, M. R. JR., Amin, R. W., Arnold, J. C. and Nachlas, J. A (1988), “ charts with variable sampling intervals,” Technometrics, 30(2), 181-192.[18] Roberts, S. W. (1959), “Control chart tests based on geometric moving averages,” Technometrics, 1, 239-250.[19] Saccucci, M. S. and Lucas, J. M. (1990), “Average run length for exponentially weighted moving average control schemes using the markov chain approach,” Journal of Quality Technology, 22, 154-162.[20] Yang, S. F., Cheng, T. C., Hung, Y. C. and Cheng, S. W. (2012), “A New Chart for Monitoring Service Process Mean,” Quality and Reliability Engineering International, 28(4), 377-386 zh_TW
