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題名 韋柏分配下規格下限與X-bar 管制圖之經濟設計
Economic design of specification limit and X-bar control chart under Weibull distribution作者 蔡瑋倫
Tsai, Wei Lun貢獻者 楊素芬
蔡瑋倫
Tsai, Wei Lun關鍵詞 經濟設計
X-bar 管制圖
規格界限
韋柏分配
Economic design
X-bar control chart
Specification limit
Weibull distribution日期 2012 上傳時間 1-Jul-2013 17:00:56 (UTC+8) 摘要 To determine the economic design of control charts and the specification limits with minimum cost are two separate issues in previous research areas. In this study, we proposed a method to determine the optimal design parameters of X control charts and the specification limits simultaneously from an economic viewpoint. We also consider two types of X control charts: one is the economic X control chart and the other is the economic statistical X control chart. We obtain the optimal results by minimizing the expected cost per unit time for the-larger-the-better quality characteristic with a Weibull distribution. Weconsider the asymmetric control limits because of the asymmetric feature of theWeibull distribution. Also, we are considering the difference between monitoring the process byusing an economic statistical X control chart and conducting a complete inspection plan.Which way is better, process control or inspection plan?In our data analysis of the two types of X control chart, we find that the optimal expected cost per unit time with complete inspection is lower than without completeinspection. This is because the coefficient of Taguchi’s quadratic loss function we set is too small. And the analysis shows us the significant parameters for the optimal expected cost per unit time and design parameters.At last, in our numerical examples for two different types of X control chart, we find that the performance of the economic X control chart is as good as the economic statistical one. However, we suggest the producer use the economic statistical X control chart with a complete inspection plan to obtain a lower expected cost per unit time and larger power of the control chart. 參考文獻 [1] Ardia, D., Mullen, K., Peterson, B. and Ulrich, J. (2012), DEoptim: Differential evolution optimization in R. version 2.2-1. URL http://CRAN.R-project.org/package=DEoptim.[2] Chen, Y.K. and Chiou, K.C. (2005), “Optimal design of VSI X control charts for monitoring correlated samples,” Quality and Reliability Engineering International, 21(8), 757-768.[3] Chen, C.H. and Khoo, M.B.C. (2008), “Joint determination of optimum process mean and economic specification limits for rectifying inspection plan with inspection error,”Journal of the Chinese Institute of Industrial Engineers, 25(5), 389-398.[4] Cho, B. R. and Phillips, M. D. (1998), “Design of the optimum product specifications for S-type quality characteristics,” International Journal of Production Research, 36(2), 459-474.[5] Chou, C. Y., Chen, C.H. and Chen, C.H. (2006b), “Economic design of variable sampling intervals T-square control charts using genetic algorithms,” Expert Systemswith Applications, 30(2), 233-242.[6] Chou, C.Y., Chen, C.H. and Liu, H.R. (2006a), “Economic design of EWMA charts with variable sampling intervals,” Quality and Quantity, 40(6), 879-896.[7] Chou, C.Y., Liu, H.R., Chen, C.H. and Huang, X.R. (2002), “Economic-statistical design of multivariate control charts using quality loss function,” AdvancedManufacturing Technology, 20(12), 916-924.[8] Duncan, A. J. (1956), “The economic design of X charts used to maintain current control of a process,” Journal of the American Statistical Association, 51(274),228-242.[9] Duncan, A. J. (1971), “The economic design of X charts when there is a multiplicity of assignable causes,” Journal of the American Statistical Association, 66(333),107-121.[10] Dutang, C., Goulet, V. and Pigeon, M. (2008), “actuar: An R package for actuarial science,” Journal of Statistical Software, 25(7), 1-37.[11] Elsayed, E.A. and Chen, A. (1994), “An economic design of X control chart using quadratic loss function,” International Journal of Production Research, 32(4),873-887.[12] Erto, P., Pallotta, G. and Park, S. H. (2008), “An example of data technology product: a control chart for Weibull processes,” International Statistical Review, 76(2), 157-166.[13] Feng, Q. and Kapur, K.C. (2006), “Economic development of specifications for 100% inspection based on asymmetric quality loss function,” IIE Transactions, 38(8),659-669.[14] Filho, J. C. S. S. and Yacoub, M. D. (2006), “Simple precise approximations to Weibull sums,” IEEE Communications Letters, 10(8), 614-616.[15] Kapur, K.C. (1988), “An approach for development of specifications for quality improvement,” Quality Engineering, 1(1), 63-77.[16] Kapur, K.C. and Cho, B.R. (1994), “Economic design and development of specifications,” Quality Engineering, 6(3), 401-417.[17] Lorenzen, T. J. and Vance, L. C. (1986), “The economic design of control charts: a unified approach,” Technometrics, 28(1), 3-10.[18] Montgomery, D. C. (1980), “The economic design of control charts: a review and literature survey,” Journal of Quality Technology, 12(2), 75-87.[19] Panagos, M. R., Heikes, R. G. and Montgomery, D. C. (1985), “Economic design of X control charts for two manufacturing process models,” Naval Research LogisticsQuarterly, 32, 631-646.[20] Phillips, M. D. and Cho, B. R. (1998), “An empirical approach to designing product specifications: A case study,” Quality Engineering, 11(1), 91-100.[21] R Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URLhttp://www.R-project.org/.[22] Taguchi, G. (1984), “The role of metrological control for quality control,” Proceedings of the International Symposium on Metrology for Quality Control in Production, 1-7.[23] Tang, K. (1988), “Economic design of product specifications for a complete inspection plan,” International Journal of Production Research, 26(2), 203-217.[24] Torng, C.C., Lee, P.H. and Liao, N.Y. (2009), “An economic-statistical design of double sampling X control chart,” International Journal of Production Economics,120(2), 495-500.[25] Vommi, V.B. and Seetala, M.S.N. (2007), “A new approach to robust economic design of control charts,” Applied Soft Computing, 7(1), 211-228.[26] Yang, S.F. and Rahim, M.A. (2005), “Economic statistical process control for multivariate quality characteristics under Weibull shock model,” International Journal of Production Economics, 98(2), 215-226.[27] Yu, F.J. and Hou, J.L. (2006), “Optimization of design parameters for X control charts with multiple assignable causes,” Journal of Applied Statistics, 33(3), 279-290. 描述 碩士
國立政治大學
統計研究所
99354006
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099354006 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.author (Authors) 蔡瑋倫 zh_TW dc.contributor.author (Authors) Tsai, Wei Lun en_US dc.creator (作者) 蔡瑋倫 zh_TW dc.creator (作者) Tsai, Wei Lun en_US dc.date (日期) 2012 en_US dc.date.accessioned 1-Jul-2013 17:00:56 (UTC+8) - dc.date.available 1-Jul-2013 17:00:56 (UTC+8) - dc.date.issued (上傳時間) 1-Jul-2013 17:00:56 (UTC+8) - dc.identifier (Other Identifiers) G0099354006 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58663 - 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) 99354006 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) To determine the economic design of control charts and the specification limits with minimum cost are two separate issues in previous research areas. In this study, we proposed a method to determine the optimal design parameters of X control charts and the specification limits simultaneously from an economic viewpoint. We also consider two types of X control charts: one is the economic X control chart and the other is the economic statistical X control chart. We obtain the optimal results by minimizing the expected cost per unit time for the-larger-the-better quality characteristic with a Weibull distribution. Weconsider the asymmetric control limits because of the asymmetric feature of theWeibull distribution. Also, we are considering the difference between monitoring the process byusing an economic statistical X control chart and conducting a complete inspection plan.Which way is better, process control or inspection plan?In our data analysis of the two types of X control chart, we find that the optimal expected cost per unit time with complete inspection is lower than without completeinspection. This is because the coefficient of Taguchi’s quadratic loss function we set is too small. And the analysis shows us the significant parameters for the optimal expected cost per unit time and design parameters.At last, in our numerical examples for two different types of X control chart, we find that the performance of the economic X control chart is as good as the economic statistical one. However, we suggest the producer use the economic statistical X control chart with a complete inspection plan to obtain a lower expected cost per unit time and larger power of the control chart. en_US dc.description.tableofcontents CHAPTER 1. INTRODUCTION.............................................. 11.1 Research Motivation................................... 11.2 Literature Review..................................... 21.3 Research Method ...................................... 4CHAPTER 2. ECONOMIC DESIGN OF A X CONTROL CHART FOR APROCESS WITH WEIBULL DATA................................. 62.1 Approximated In-Control Sampling Distribution of the X under Weibull Distribution.................................62.2 Approximated Out-of-Control Sampling Distribution of X under Weibull Distribution................................ 92.3 Construction of Economic X Probability Chart Based on X Sampling Distribution92.4 The Calculation of alpha and beta ................... 102.5 Derivation of Expected Cycle Time ................... 102.6 Derivation of the Expected Cycle Cost ............... 122.7 Determination of the Optimum Sampling Interval of the Economic X Control Chart.................................142.8 Data Analysis and Resulting Comparison to Different Out-of-Control Distributions ............................15CHAPTER 3. DESIGN OF ECONOMIC X CHART AND INSPECTIONSPECIFICATION LIMIT FOR A PROCESS WITH WEIBULL DATA.......203.1 Derivation of the Expected Cycle Cost ................203.2 Determination of the Optimum Specification Limit and Design Parameters of the Economic X Control Chart ....... 223.3 Data Analysis and the Result Comparisons with and without the Inspection Plan ............................. 223.4 An Example .......................................... 283.4.1 Data .............................................. 283.4.2 Estimating the in-control parameters of the Weibull distribution ............................................ 293.4.3 Simulation Data for Out-of-control Distribution ......................................................... 303.4.4 Constructing the economic X control chart and inspection plan ......................................... 31CHAPTER 4. ECONOMIC STATISTICAL DESIGN OF THE X CHART FORTHE PROCESS USING WEIBULL DATA........................... 334.1 Construction of the Economic Statistical X Chart Based on the X Sampling Distribution and Determination of the Optimum Design Parameters of the Economic Statistical X Control Chart............................................ 334.2 Data Analysis and Result Comparisons for the Different Out-of-control Distributions ............................ 34CHAPTER 5. DETERMINATION OF THE INSPECTION SPECIFICATION ANDECONOMIC STATISTICAL X CHART FOR A PROCESS WITHWEIBULL DATA ............................................ 405.1 Determination of the Optimum Specification Limit and Design Parameters of the Economic Statistical X Control Chart ................................................... 405.2 Data Analysis and Result Comparisons with and without the Inspection Plan ..................................... 405.3 An Example .......................................... 475.3.1 Obtaining the range of the UCL and LCL............. 475.3.2 Constructing the economic statistical X control chart and inspection plan ..................................... 475.3.3 Comparison of the economic X control chart with inspection plan and the economic statistical X control chart with inspection plan............................... 49CHAPTER 6. COSTS COMPARISON OF THE PROCESS QUALITY CONTROLAND PRODUCT INSPECTION................................... 516.1 Derivation of The Expected Cycle Cost ............... 516.1.1 The cost for process control in the observing time OT....................................................... 516.1.2 The total cost for product inspection in observing time OT ................................................. 526.2 Data Analysis and Comparing the Results with Different In-control Weibull Distributions ........................ 536.2.1 Cost for process control........................... 536.2.2 Cost for production inspection .................... 596.3 Analysis for the Cost Difference..................... 64CHAPTER 7. CONCLUSION AND RECOMMENDATIONS FOR FUTURE STUDY76REFERENCES .............................................. 78 zh_TW dc.format.extent 1872456 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099354006 en_US dc.subject (關鍵詞) 經濟設計 zh_TW dc.subject (關鍵詞) X-bar 管制圖 zh_TW dc.subject (關鍵詞) 規格界限 zh_TW dc.subject (關鍵詞) 韋柏分配 zh_TW dc.subject (關鍵詞) Economic design en_US dc.subject (關鍵詞) X-bar control chart en_US dc.subject (關鍵詞) Specification limit en_US dc.subject (關鍵詞) Weibull distribution en_US dc.title (題名) 韋柏分配下規格下限與X-bar 管制圖之經濟設計 zh_TW dc.title (題名) Economic design of specification limit and X-bar control chart under Weibull distribution en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1] Ardia, D., Mullen, K., Peterson, B. and Ulrich, J. (2012), DEoptim: Differential evolution optimization in R. version 2.2-1. URL http://CRAN.R-project.org/package=DEoptim.[2] Chen, Y.K. and Chiou, K.C. (2005), “Optimal design of VSI X control charts for monitoring correlated samples,” Quality and Reliability Engineering International, 21(8), 757-768.[3] Chen, C.H. and Khoo, M.B.C. (2008), “Joint determination of optimum process mean and economic specification limits for rectifying inspection plan with inspection error,”Journal of the Chinese Institute of Industrial Engineers, 25(5), 389-398.[4] Cho, B. R. and Phillips, M. D. (1998), “Design of the optimum product specifications for S-type quality characteristics,” International Journal of Production Research, 36(2), 459-474.[5] Chou, C. Y., Chen, C.H. and Chen, C.H. (2006b), “Economic design of variable sampling intervals T-square control charts using genetic algorithms,” Expert Systemswith Applications, 30(2), 233-242.[6] Chou, C.Y., Chen, C.H. and Liu, H.R. (2006a), “Economic design of EWMA charts with variable sampling intervals,” Quality and Quantity, 40(6), 879-896.[7] Chou, C.Y., Liu, H.R., Chen, C.H. and Huang, X.R. (2002), “Economic-statistical design of multivariate control charts using quality loss function,” AdvancedManufacturing Technology, 20(12), 916-924.[8] Duncan, A. J. (1956), “The economic design of X charts used to maintain current control of a process,” Journal of the American Statistical Association, 51(274),228-242.[9] Duncan, A. J. (1971), “The economic design of X charts when there is a multiplicity of assignable causes,” Journal of the American Statistical Association, 66(333),107-121.[10] Dutang, C., Goulet, V. and Pigeon, M. (2008), “actuar: An R package for actuarial science,” Journal of Statistical Software, 25(7), 1-37.[11] Elsayed, E.A. and Chen, A. (1994), “An economic design of X control chart using quadratic loss function,” International Journal of Production Research, 32(4),873-887.[12] Erto, P., Pallotta, G. and Park, S. H. (2008), “An example of data technology product: a control chart for Weibull processes,” International Statistical Review, 76(2), 157-166.[13] Feng, Q. and Kapur, K.C. (2006), “Economic development of specifications for 100% inspection based on asymmetric quality loss function,” IIE Transactions, 38(8),659-669.[14] Filho, J. C. S. S. and Yacoub, M. D. (2006), “Simple precise approximations to Weibull sums,” IEEE Communications Letters, 10(8), 614-616.[15] Kapur, K.C. (1988), “An approach for development of specifications for quality improvement,” Quality Engineering, 1(1), 63-77.[16] Kapur, K.C. and Cho, B.R. (1994), “Economic design and development of specifications,” Quality Engineering, 6(3), 401-417.[17] Lorenzen, T. J. and Vance, L. C. (1986), “The economic design of control charts: a unified approach,” Technometrics, 28(1), 3-10.[18] Montgomery, D. C. (1980), “The economic design of control charts: a review and literature survey,” Journal of Quality Technology, 12(2), 75-87.[19] Panagos, M. R., Heikes, R. G. and Montgomery, D. C. (1985), “Economic design of X control charts for two manufacturing process models,” Naval Research LogisticsQuarterly, 32, 631-646.[20] Phillips, M. D. and Cho, B. R. (1998), “An empirical approach to designing product specifications: A case study,” Quality Engineering, 11(1), 91-100.[21] R Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URLhttp://www.R-project.org/.[22] Taguchi, G. (1984), “The role of metrological control for quality control,” Proceedings of the International Symposium on Metrology for Quality Control in Production, 1-7.[23] Tang, K. (1988), “Economic design of product specifications for a complete inspection plan,” International Journal of Production Research, 26(2), 203-217.[24] Torng, C.C., Lee, P.H. and Liao, N.Y. (2009), “An economic-statistical design of double sampling X control chart,” International Journal of Production Economics,120(2), 495-500.[25] Vommi, V.B. and Seetala, M.S.N. (2007), “A new approach to robust economic design of control charts,” Applied Soft Computing, 7(1), 211-228.[26] Yang, S.F. and Rahim, M.A. (2005), “Economic statistical process control for multivariate quality characteristics under Weibull shock model,” International Journal of Production Economics, 98(2), 215-226.[27] Yu, F.J. and Hou, J.L. (2006), “Optimization of design parameters for X control charts with multiple assignable causes,” Journal of Applied Statistics, 33(3), 279-290. zh_TW
