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題名 最小成本下，規格及X-bar-S管制圖之設計
The design of specification and X-bar-S charts with minimal cost作者 沈依潔
Shen, I Chieh貢獻者 楊素芬
沈依潔
Shen, I Chieh關鍵詞 經濟統計管制圖
顧客允差
生產者允差
X-bar-S管制圖
損失函數
Economic statistical control charts
Consumer tolerance
Producer tolerance
X-bar and S charts
Loss function日期 2011 上傳時間 30-十月-2012 10:13:37 (UTC+8) 摘要 最小成本下，規格及X-bar-S管制圖之設計
The design of economic statistical control charts and specification are both crucial research areas in industry. Furthermore, the determination of consumer and producer specifications is important to producer. In this study, we consider eight cost models including the consumer loss function and/or the producer loss function with the economic statistical X-bar and S charts or Shewhart-type economic X-bar and S charts. To determine the design parameters of the X-bar and S charts and consumer tolerance and/or producer tolerance, we using the Genetic Algorithm to minimizing expected cost per unit time. In the comparison of examples and sensitivity analyses, we found that the optimal design parameters of the Shewhart-type economic X-bar and S charts are similar to those of economic statistical X-bar and S control charts, and the expected cost per unit time may lower than the actual cost per unit time when the cost model only considering consumer loss or producer loss. When considering both consumer and producer tolerances in the cost model, the design parameters of the economic X-bar and S charts are not sensitive to the cost models. If the producer tolerance is smaller than the consumer tolerance, and the producer loss is smaller than the consumer loss, the optimal producer tolerance should be small.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] Collani, V. and Sheil, J. (1989), “An approach to controlling process variability”, Journal of Quality Technology, Vol. 24, pp. 87-96.[3] Duncan, A. (1956), “The economic design of chart used to maintain current control of a process”, Journal of The American Statistical Association, Vol. 51, pp.228-242.[4] Duncan, A. (1974), Quality Control and Industrial Statistics, Richard D. Irwin, Homewood, IL.[5] Elsayed, E. and Chen, A. (1994), “An economic design of control charts using quadratic loss function”, International Journal of Production Research, Vol. 32, pp. 873-887.[6] Fathi, Y. (1990),“Producer-consumer tolerances”, Journal of Quality Technology, Vol. 22, No. 2, pp. 138-145.[7] Feng, Q. and Kapur, K. (2006), “Economic development of specifications for 100% inspection based on asymmetric quality loss function”, Quality Technology & Quantitative Management, Vol. 3, No. 2, pp. 127-144.[8] Kapur, K. (1988), “An approach for development of specifications for quality improvement”, Quality Engineering, Vol. 1, No.1, pp. 63-77.[9] Lee, M., Kim, S., Kwon, H., and Hong, S. (2004), “Economic selection of mean value for a filling process under quadratic quality loss”, International Journal of Reliability, Quality and Safety Engineering, Vol. 11, No. 1, pp. 81-90.[10] Maghsoodloo S. and Li M. (2000), “Optimal asymmetric tolerance design”, IIE Transactions, Vol. 32, No. 12, pp. 1127-1137.[11] Montgomery, D. (1980), “The economic design of control charts: a review and literature survey”, Journal of Quality Technology, Vol. 21, pp. 65-70.[12] Montgomery, D. (1985), ”Economic design of control charts for two manufacturing process models”, Naval Research Logistics Quarterly, Vol. 32, pp.531-646.[13] Rahim, R., Lashkari, R. and Banerjee, P. (1988), “Joint economic design of mean and variance control charts”, Engineer Optimization, Vol. 14, pp.65-78.[14] Saniga, E. (1979), “Statistical control chart design with an application to and R control charts”, Management Science, Vol. 31, pp.313-320.[15] Tang, K. (1988), “Economic design of product specifications for a complete inspection plan”, International Journal of Production Research, Vol. 26, No. 2, pp. 203-217.[16] Woodall, W. (1986), “Weaknesses of the economic design of control charts”, Technometrics, Vol. 28, pp. 408-409.[17] Woodall, W. (1987), “Conflicts between Deming’s philosophy and the economic design of control charts”, Frontiers in Statistical Quality Control, Vol. 3, pp. 242-248.[18] Yang, S. (1997), “An optimal design of joint and S control charts using quadratic loss function”, International Journal of Quality & Reliability Management, Vol. 14, No. 9, pp.948-966. 描述 碩士
國立政治大學
統計研究所
99354026
100資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099354026 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.author (作者) 沈依潔 zh_TW dc.contributor.author (作者) Shen, I Chieh en_US dc.creator (作者) 沈依潔 zh_TW dc.creator (作者) Shen, I Chieh en_US dc.date (日期) 2011 en_US dc.date.accessioned 30-十月-2012 10:13:37 (UTC+8) - dc.date.available 30-十月-2012 10:13:37 (UTC+8) - dc.date.issued (上傳時間) 30-十月-2012 10:13:37 (UTC+8) - dc.identifier (其他 識別碼) G0099354026 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54173 - 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) 99354026 zh_TW dc.description (描述) 100 zh_TW dc.description.abstract (摘要) 最小成本下，規格及X-bar-S管制圖之設計 zh_TW dc.description.abstract (摘要) The design of economic statistical control charts and specification are both crucial research areas in industry. Furthermore, the determination of consumer and producer specifications is important to producer. In this study, we consider eight cost models including the consumer loss function and/or the producer loss function with the economic statistical X-bar and S charts or Shewhart-type economic X-bar and S charts. To determine the design parameters of the X-bar and S charts and consumer tolerance and/or producer tolerance, we using the Genetic Algorithm to minimizing expected cost per unit time. In the comparison of examples and sensitivity analyses, we found that the optimal design parameters of the Shewhart-type economic X-bar and S charts are similar to those of economic statistical X-bar and S control charts, and the expected cost per unit time may lower than the actual cost per unit time when the cost model only considering consumer loss or producer loss. When considering both consumer and producer tolerances in the cost model, the design parameters of the economic X-bar and S charts are not sensitive to the cost models. If the producer tolerance is smaller than the consumer tolerance, and the producer loss is smaller than the consumer loss, the optimal producer tolerance should be small. en_US dc.description.tableofcontents 1. INTRODUCTION AND LITERATURE REVIEW 12. DESIGN OF ECONOMIC STATISTICAL x ̅ AND S CHARTS WITHOUT TOLERANCE 42.1 Derivation of Cost Models 42.2 An Example and Numerical Analysis 82.2.1 Example 82.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 122.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 142.3 Sensitivity Analysis 163. DESIGN OF CONSUMER TOLERANCE AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 213.1 Derivation of Cost Models 213.2 An Example and Numerical Analysis 233.2.1 Example 233.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 272.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 293.3 Sensitivity Analysis 314. DESIGN OF PRODUCER TOLERANCE AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 364.1 Derivation of Cost Models 364.2 An Example and Numerical Analysis 384.2.1 Example 384.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 424.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 444.3 Sensitivity Analysis 465. DESIGN OF CONSUMER TOLERANCE, PRODUCER TOLERANCE, AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 515.1 Consumer and Producer Loss Functions Are the Same but with Smaller Producer Tolerance 515.1.1 Derivation of Cost Models 515.1.2 An Example and Numerical Analysis 535.1.2.1 Example 535.1.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 575.1.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 595.1.3 Sensitivity Analysis 615.2 Considering Different Consumer and Producer Loss Functions with Smaller Consumer Tolerance 655.2.1 Derivation of Cost Models 655.2.2 An Example and Numerical Analysis 675.2.2.1 Example 675.2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 715.2.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 735.2.3 Sensitivity Analysis 755.3 Considering Different Consumer and Producer Loss Functions with a Larger Consumer Tolerance 805.3.1 Smaller Coefficients of Consumer Loss Functions and Larger Consumer Tolerance 805.3.2 Larger Coefficient of Consumer Loss Function With Larger Consumer Tolerance 825.3.2.1 Derivation of Cost Models 825.3.2.2 An Example and Numerical Analysis 845.3.2.2.1 Example 845.3.2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 895.3.2.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 915.3.2.3 Sensitivity Analysis 935.3.3 Equal Consumer Loss Function and Producer Loss Function Coefficients but With Larger Consumer Tolerance 975.3.3.1 Derivation of Cost Models 975.3.3.2 An Example and Numerical Analysis 995.3.3.2.1 Example 995.3.3.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 1035.3.3.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 1055.3.3.3 Sensitivity Analysis 1076. EXAMPLES AND SENSITIVE ANALYSIS COMPARISON FOR ALL TYPES OF LOSS FUNCTIONS 1116.1 Examples Comparison 1116.2 Sensitivity Analysis Comparison 1137. CONCLUSION 1188. REFERENCE 120 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099354026 en_US dc.subject (關鍵詞) 經濟統計管制圖 zh_TW dc.subject (關鍵詞) 顧客允差 zh_TW dc.subject (關鍵詞) 生產者允差 zh_TW dc.subject (關鍵詞) X-bar-S管制圖 zh_TW dc.subject (關鍵詞) 損失函數 zh_TW dc.subject (關鍵詞) Economic statistical control charts en_US dc.subject (關鍵詞) Consumer tolerance en_US dc.subject (關鍵詞) Producer tolerance en_US dc.subject (關鍵詞) X-bar and S charts en_US dc.subject (關鍵詞) Loss function en_US dc.title (題名) 最小成本下，規格及X-bar-S管制圖之設計 zh_TW dc.title (題名) The design of specification and X-bar-S charts with minimal cost 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] Collani, V. and Sheil, J. (1989), “An approach to controlling process variability”, Journal of Quality Technology, Vol. 24, pp. 87-96.[3] Duncan, A. (1956), “The economic design of chart used to maintain current control of a process”, Journal of The American Statistical Association, Vol. 51, pp.228-242.[4] Duncan, A. (1974), Quality Control and Industrial Statistics, Richard D. Irwin, Homewood, IL.[5] Elsayed, E. and Chen, A. (1994), “An economic design of control charts using quadratic loss function”, International Journal of Production Research, Vol. 32, pp. 873-887.[6] Fathi, Y. (1990),“Producer-consumer tolerances”, Journal of Quality Technology, Vol. 22, No. 2, pp. 138-145.[7] Feng, Q. and Kapur, K. (2006), “Economic development of specifications for 100% inspection based on asymmetric quality loss function”, Quality Technology & Quantitative Management, Vol. 3, No. 2, pp. 127-144.[8] Kapur, K. (1988), “An approach for development of specifications for quality improvement”, Quality Engineering, Vol. 1, No.1, pp. 63-77.[9] Lee, M., Kim, S., Kwon, H., and Hong, S. (2004), “Economic selection of mean value for a filling process under quadratic quality loss”, International Journal of Reliability, Quality and Safety Engineering, Vol. 11, No. 1, pp. 81-90.[10] Maghsoodloo S. and Li M. (2000), “Optimal asymmetric tolerance design”, IIE Transactions, Vol. 32, No. 12, pp. 1127-1137.[11] Montgomery, D. (1980), “The economic design of control charts: a review and literature survey”, Journal of Quality Technology, Vol. 21, pp. 65-70.[12] Montgomery, D. (1985), ”Economic design of control charts for two manufacturing process models”, Naval Research Logistics Quarterly, Vol. 32, pp.531-646.[13] Rahim, R., Lashkari, R. and Banerjee, P. (1988), “Joint economic design of mean and variance control charts”, Engineer Optimization, Vol. 14, pp.65-78.[14] Saniga, E. (1979), “Statistical control chart design with an application to and R control charts”, Management Science, Vol. 31, pp.313-320.[15] Tang, K. (1988), “Economic design of product specifications for a complete inspection plan”, International Journal of Production Research, Vol. 26, No. 2, pp. 203-217.[16] Woodall, W. (1986), “Weaknesses of the economic design of control charts”, Technometrics, Vol. 28, pp. 408-409.[17] Woodall, W. (1987), “Conflicts between Deming’s philosophy and the economic design of control charts”, Frontiers in Statistical Quality Control, Vol. 3, pp. 242-248.[18] Yang, S. (1997), “An optimal design of joint and S control charts using quadratic loss function”, International Journal of Quality & Reliability Management, Vol. 14, No. 9, pp.948-966. zh_TW
