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| Title | 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 |
| Creator | 沈依潔 Shen, I Chieh |
| Contributor | 楊素芬 沈依潔 Shen, I Chieh |
| Key Words | 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 |
| Date | 2011 |
| Date Issued | 30-Oct-2012 10:13:37 (UTC+8) |
| Summary | 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. |
| Description | 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 |
| Type | thesis |
| dc.contributor.advisor | 楊素芬 | zh_TW |
| dc.contributor.author (Authors) | 沈依潔 | zh_TW |
| dc.contributor.author (Authors) | 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-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) | 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 1 2. DESIGN OF ECONOMIC STATISTICAL x ̅ AND S CHARTS WITHOUT TOLERANCE 4 2.1 Derivation of Cost Models 4 2.2 An Example and Numerical Analysis 8 2.2.1 Example 8 2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 12 2.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 14 2.3 Sensitivity Analysis 16 3. DESIGN OF CONSUMER TOLERANCE AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 21 3.1 Derivation of Cost Models 21 3.2 An Example and Numerical Analysis 23 3.2.1 Example 23 3.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 27 2.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 29 3.3 Sensitivity Analysis 31 4. DESIGN OF PRODUCER TOLERANCE AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 36 4.1 Derivation of Cost Models 36 4.2 An Example and Numerical Analysis 38 4.2.1 Example 38 4.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 42 4.2.3 Determining Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 44 4.3 Sensitivity Analysis 46 5. DESIGN OF CONSUMER TOLERANCE, PRODUCER TOLERANCE, AND ECONOMIC STATISTICAL X ̅ AND S CHARTS 51 5.1 Consumer and Producer Loss Functions Are the Same but with Smaller Producer Tolerance 51 5.1.1 Derivation of Cost Models 51 5.1.2 An Example and Numerical Analysis 53 5.1.2.1 Example 53 5.1.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 57 5.1.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 59 5.1.3 Sensitivity Analysis 61 5.2 Considering Different Consumer and Producer Loss Functions with Smaller Consumer Tolerance 65 5.2.1 Derivation of Cost Models 65 5.2.2 An Example and Numerical Analysis 67 5.2.2.1 Example 67 5.2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 71 5.2.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 73 5.2.3 Sensitivity Analysis 75 5.3 Considering Different Consumer and Producer Loss Functions with a Larger Consumer Tolerance 80 5.3.1 Smaller Coefficients of Consumer Loss Functions and Larger Consumer Tolerance 80 5.3.2 Larger Coefficient of Consumer Loss Function With Larger Consumer Tolerance 82 5.3.2.1 Derivation of Cost Models 82 5.3.2.2 An Example and Numerical Analysis 84 5.3.2.2.1 Example 84 5.3.2.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 89 5.3.2.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 91 5.3.2.3 Sensitivity Analysis 93 5.3.3 Equal Consumer Loss Function and Producer Loss Function Coefficients but With Larger Consumer Tolerance 97 5.3.3.1 Derivation of Cost Models 97 5.3.3.2 An Example and Numerical Analysis 99 5.3.3.2.1 Example 99 5.3.3.2.2 The Effects of Optimal Design Parameters under Different Combination δ and σ for a Given In-control Distribution 103 5.3.3.2.3 Determine Optimal in Control Distribution with Minimum Expected Cost Per Unit Time 105 5.3.3.3 Sensitivity Analysis 107 6. EXAMPLES AND SENSITIVE ANALYSIS COMPARISON FOR ALL TYPES OF LOSS FUNCTIONS 111 6.1 Examples Comparison 111 6.2 Sensitivity Analysis Comparison 113 7. CONCLUSION 118 8. 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 |