1. NCCU Academic Hub
  2. Publications
  3. College of Commerce
  4. Theses
  5. Item

Publications-Theses

Article View/Open

Publication Export

Google ScholarTM

NCCU Library

Citation Infomation

Related Publications in TAIR

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-Oct-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.\n[2] Collani, V. and Sheil, J. (1989), “An approach to controlling process variability”, Journal of Quality Technology, Vol. 24, pp. 87-96.\n[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.\n[4] Duncan, A. (1974), Quality Control and Industrial Statistics, Richard D. Irwin, Homewood, IL.\n[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.\n[6] Fathi, Y. (1990),“Producer-consumer tolerances”, Journal of Quality Technology, Vol. 22, No. 2, pp. 138-145.\n[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.\n[8] Kapur, K. (1988), “An approach for development of specifications for quality improvement”, Quality Engineering, Vol. 1, No.1, pp. 63-77.\n[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.\n[10] Maghsoodloo S. and Li M. (2000), “Optimal asymmetric tolerance design”, IIE Transactions, Vol. 32, No. 12, pp. 1127-1137.\n[11] Montgomery, D. (1980), “The economic design of control charts: a review and literature survey”, Journal of Quality Technology, Vol. 21, pp. 65-70.\n[12] Montgomery, D. (1985), ”Economic design of control charts for two manufacturing process models”, Naval Research Logistics Quarterly, Vol. 32, pp.531-646.\n[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.\n[14] Saniga, E. (1979), “Statistical control chart design with an application to and R control charts”, Management Science, Vol. 31, pp.313-320.\n[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.\n[16] Woodall, W. (1986), “Weaknesses of the economic design of control charts”, Technometrics, Vol. 28, pp. 408-409.\n[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.\n[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 (Authors) 沈依潔zh_TW
dc.contributor.author (Authors) Shen, I Chiehen_US
dc.creator (作者) 沈依潔zh_TW
dc.creator (作者) Shen, I Chiehen_US
dc.date (日期) 2011en_US
dc.date.accessioned 30-Oct-2012 10:13:37 (UTC+8)-
dc.date.available 30-Oct-2012 10:13:37 (UTC+8)-
dc.date.issued (上傳時間) 30-Oct-2012 10:13:37 (UTC+8)-
dc.identifier (Other Identifiers) G0099354026en_US
dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=61646-
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) 99354026zh_TW
dc.description (描述) 100zh_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 1\n2. DESIGN OF ECONOMIC STATISTICAL x ̅ AND S CHARTS WITHOUT TOLERANCE 4\n2.1 Derivation of Cost Models 4\n2.2 An Example and Numerical Analysis 8\n2.2.1 Example 8\n2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 12\n2.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 14\n2.3 Sensitivity Analysis 16\n3. DESIGN OF CONSUMER TOLERANCE AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 21\n3.1 Derivation of Cost Models 21\n3.2 An Example and Numerical Analysis 23\n3.2.1 Example 23\n3.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 27\n2.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 29\n3.3 Sensitivity Analysis 31\n4. DESIGN OF PRODUCER TOLERANCE AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 36\n4.1 Derivation of Cost Models 36\n4.2 An Example and Numerical Analysis 38\n4.2.1 Example 38\n4.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 42\n4.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 44\n4.3 Sensitivity Analysis 46\n5. DESIGN OF CONSUMER TOLERANCE, PRODUCER TOLERANCE, AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 51\n5.1 Consumer and Producer Loss Functions Are the Same but with Smaller Producer Tolerance 51\n5.1.1 Derivation of Cost Models 51\n5.1.2 An Example and Numerical Analysis 53\n5.1.2.1 Example 53\n5.1.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 57\n5.1.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 59\n5.1.3 Sensitivity Analysis 61\n5.2 Considering Different Consumer and Producer Loss Functions with Smaller Consumer Tolerance 65\n5.2.1 Derivation of Cost Models 65\n5.2.2 An Example and Numerical Analysis 67\n5.2.2.1 Example 67\n5.2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 71\n5.2.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 73\n5.2.3 Sensitivity Analysis 75\n5.3 Considering Different Consumer and Producer Loss Functions with a Larger Consumer Tolerance 80\n5.3.1 Smaller Coefficients of Consumer Loss Functions and Larger Consumer Tolerance 80\n5.3.2 Larger Coefficient of Consumer Loss Function With Larger Consumer Tolerance 82\n5.3.2.1 Derivation of Cost Models 82\n5.3.2.2 An Example and Numerical Analysis 84\n5.3.2.2.1 Example 84\n5.3.2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 89\n5.3.2.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 91\n5.3.2.3 Sensitivity Analysis 93\n5.3.3 Equal Consumer Loss Function and Producer Loss Function Coefficients but With Larger Consumer Tolerance 97\n5.3.3.1 Derivation of Cost Models 97\n5.3.3.2 An Example and Numerical Analysis 99\n5.3.3.2.1 Example 99\n5.3.3.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 103\n5.3.3.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 105\n5.3.3.3 Sensitivity Analysis 107\n6. EXAMPLES AND SENSITIVE ANALYSIS COMPARISON FOR ALL TYPES OF LOSS FUNCTIONS 111\n6.1 Examples Comparison 111\n6.2 Sensitivity Analysis Comparison 113\n7. CONCLUSION 118\n8. REFERENCE 120zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099354026en_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 chartsen_US
dc.subject (關鍵詞) Consumer toleranceen_US
dc.subject (關鍵詞) Producer toleranceen_US
dc.subject (關鍵詞) X-bar and S chartsen_US
dc.subject (關鍵詞) Loss functionen_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 costen_US
dc.type (資料類型) thesisen
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.\n[2] Collani, V. and Sheil, J. (1989), “An approach to controlling process variability”, Journal of Quality Technology, Vol. 24, pp. 87-96.\n[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.\n[4] Duncan, A. (1974), Quality Control and Industrial Statistics, Richard D. Irwin, Homewood, IL.\n[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.\n[6] Fathi, Y. (1990),“Producer-consumer tolerances”, Journal of Quality Technology, Vol. 22, No. 2, pp. 138-145.\n[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.\n[8] Kapur, K. (1988), “An approach for development of specifications for quality improvement”, Quality Engineering, Vol. 1, No.1, pp. 63-77.\n[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.\n[10] Maghsoodloo S. and Li M. (2000), “Optimal asymmetric tolerance design”, IIE Transactions, Vol. 32, No. 12, pp. 1127-1137.\n[11] Montgomery, D. (1980), “The economic design of control charts: a review and literature survey”, Journal of Quality Technology, Vol. 21, pp. 65-70.\n[12] Montgomery, D. (1985), ”Economic design of control charts for two manufacturing process models”, Naval Research Logistics Quarterly, Vol. 32, pp.531-646.\n[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.\n[14] Saniga, E. (1979), “Statistical control chart design with an application to and R control charts”, Management Science, Vol. 31, pp.313-320.\n[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.\n[16] Woodall, W. (1986), “Weaknesses of the economic design of control charts”, Technometrics, Vol. 28, pp. 408-409.\n[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.\n[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