學術產出-學位論文
| 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 | 30-十月-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 (作者) | 蔡佳宏 | zh_TW |
| dc.contributor.author (作者) | 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 | 30-十月-2012 10:13:35 (UTC+8) | - |
| dc.date.available | 30-十月-2012 10:13:35 (UTC+8) | - |
| dc.date.issued (上傳時間) | 30-十月-2012 10:13:35 (UTC+8) | - |
| dc.identifier (其他 識別碼) | 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 1 1.1 Research Motivation 1 1.2 Literature Review 1 1.3 Research Method 3 CHAPTER 2. THE SMALLER THE BETTER QUALITY VARIABLE WITH GAMMA DISTRIBUTION 4 2.1 In-control Sampling Distribution of X-bar under Gamma Distribution 4 2.2 Out-of-control Sampling Distribution of X-bar under Gamma Distribution 4 2.3 Construction of the EWMAX-bar Control Chart Based on X-bar Sampling Distribution 5 2.4 Calculation of Average Run Length for the EWMAX-bar Chart 6 2.5 Determining Control Limit Coefficient on EWMAX-bar Control Chart under Different n and λ 7 2.6 Determining the Best λ in the EWMAX-bar Chart under Different δ1, δ2 and n 11 CHAPTER 3. DERIVATION OF THE PROFIT MODEL WITHOUT PRODUCER INSPECTION 19 3.1 Derivation of Expected Cycle Time 19 3.2 Derivation of the Expected Cycle Profit 20 3.3 Determining Optimum Design Parameters of the Economic EWMAX-bar Control Chart 21 3.4 An Example 22 3.5 Sensitivity Analysis and Comparing the Results with λ=1 23 CHAPTER 4. DERIVATION OF THE PROFIT MODEL WITH PRODUCER INSPECTION 28 4.1 Derivation of the Expected Cycle Time 28 4.2 Derivation of the Expected Cycle Profit 28 4.3 Determining the Optimum Producer Inspection and Design Parameter of the Economic EWMAX-bar Control Chart 29 4.4 Example and Optimum Results Comparison for with and without Producer Inspection 30 4.5 Sensitivity Analysis and Comparing the Results of EWMAX-bar Chart with λ=1 32 CHAPTER 5. DETERMINING THE BEST λ OF THE ECONOMIC EWMAX-bar CONTROL CHART UNDER DIFFERENT SHIFT SCALES IN THE MEAN AND VARIANCE 37 5.1 Data Description and Determining the Optimum Producer Inspection and the Design Parameters of the Economic EWMAX-bar Control Chart 37 5.2 Performance Comparison of Six Numerical Examples 63 CHAPTER 6. DETERMINING THE OPTIMUM PRODUCER INSPECTION AND THE ECONOMIC VSI EWMAX-bar CONTROL CHART 65 6.1 VSI EWMAX-bar Control Chart and ATS Calculation 65 6.2 Derivation of the Profit Model without Producer Inspection 67 6.3 Derivation of the Profit Model with Producer Inspection 67 6.4 Determining Optimum Parameters of the Economic VSI EWMAX-bar Control Chart with and without producer tolerance 68 6.5 Two Numerical Examples and the Results Comparison with the FSI EWMAX-bar Control Chart 69 6.6 Sensitivity Analysis and the Optimum Results Comparison between the FSI EWMAX-bar Chart and VSI EWMAX-bar Chart 80 CHAPTER 7. SUMMARY 84 REFERENCES 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 |