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題名 生產者與中間商利潤模式有量測誤差下規格之最適設計
Optimal Design of Specification Limits under Profit Models with Measurement Errors
作者 林裕景
貢獻者 楊素芬
林裕景
關鍵詞 量測誤差
完美的維修方案
低價格銷售方案
中間商
Measurement error
Perfect repair action
Sell low price action
Middleman
日期 2012
上傳時間 1-Jul-2013 17:01:20 (UTC+8)
摘要 測量誤差在品質控制中是一個重要的議題，所以在本研究中考慮生產者的儀器具有測量誤差。當生產者的儀器具測量誤差被考慮時，我們假設生產者可採取完全的檢驗計畫或製成的控管，以保持產品的質量。我們透過比較各自的利潤選擇一個較好的品質控制政策。在完整的檢查計劃，對於不合格品我們考慮兩種方案，分別為完美的維修與以較低的價格銷售。於最大化利潤下，我們比較這兩種方案的利潤，以確定採取何種方案對生產者而言利潤會較大。
在本文中，我們也考慮一個中間商的角色。我們假定中間商與生產者的規格界限是相同的；而中間人購買的產品可能來自於生產者採取完美的維修或生產者採取以較低的價格銷售。在最大化中間商的利潤下，我們決定了中間商的規格界限，買入和賣出的價格。我們也比較這兩種方案下中間商的利潤以找出中間商應購買何種方案的商品能使其利潤最大。
在我們的分析中，我們發現，在製程中符合單位時間小生產量、高維修成本，高的不合格品成本，及高的售價時，那麼生產者應採取製程管制，否則生產者應採取完整檢驗才會使生產者具有較大的利潤。當中間商的儀器包含測量誤差時，中間商應購買的產品為來自於生產者採取完美的維修。
Measurement error is an important issue in quality control, so in this study a producer instrument with measurement error is considered. When its instrument contains measurement error, we assume that a producer takes either complete inspection or on-line process control to maintain products quality. We then compare their respective profits to choose a better quality control policy. Also in the complete inspection plan we consider perfect repair and selling at a lower price are two actions for a producer to deal with nonconforming items. Under the maximizing profit model, we determine the optimal specification limits for the producer, and then compare the profit of these two actions to determine which action is better for producer to take.
In this article we also consider the act of a middleman. We assume that the specification limits of the middleman and producer are the same and the product that middleman bought may come from perfect repair action or selling at a lower price action. When maximizing the middleman’s profit, we determine the specification limits, buying and selling price of middleman, and we also compare the profit from these two actions to find out which action is better for the middleman.
In our analysis, we found that when process has a small production per unit time, a high repair cost, a high cost of nonconforming item, and a high sell price, then process control should be preferred by producer; otherwise the producer should take complete inspection. And to have a larger profit, middleman should buy products from producer who took the action of perfect repair when middleman’s instrument contains measurement error or middleman’s instrument contains no measurement error but producer’s instrument contains a small measurement error.
參考文獻 [1] Bennett, G. K., Case, K. E., and Schmidt, J. W. (1974). The economic effects of inspection errors on attribute sampling plan. Naval Research Logistics Quarterly, 21, 431-464.
[2] Biegel, J. (1974). "Inspection errors and sampling plans". AIIE Transactions, 6(431-464).
[3] Bisgaard, S., Hunter, W. G., and Pallesen, L. (1984). "Economic selection of quality of manufactured product". Technometrics, 26, 9-18.
[4] Case, K. E. (1980). "The P control chart under inspection error". Journal of Quality Technology, 12, 1-9.
[5] Chen, C. H. (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
[6] Chen., and Chung, K. J. (1994). "Inspection error effects on economic selection of target value for a production process". European Journal of Operational Research, 79, 311-324.
[7] Chen., and Chung, K. J. (1996). "Selection of the optimal precision level and target value for a production process: the lower-specification-limit case". IIE Transactions, 28, 979-985.
[8] Crowder, S. V., and Hamilton, M. D. (1992). "An EWMA for monitoring a process standard devation". Journal of Quality Technology, 24, 12-21.
[9] Dooris, A. L. (1977). "The effect of inspection error on the operation of a c-chart". AIIE Transactions, 9, 312-315.
[10] Duffuaa, S., and Siddiqui, A. W. (2003). "Process targeting with multi-class screening and measurement error". International Journal of Production Research, 41, 1373-1391.
[11] Duncan, A. (1956). "The economic design of X-bar chart used to maintain current control of aprocess". Journal of The American Statistical Association, 51, 228-242.
[12] Fathi, Y. (1990). "Producer-consumer tolerance". Journal of Quality Technology, 22, 138-145.
[13] Feng, and Kapur. (2006). Economic design of specifications for 100% inspection with imperfect measurement systems. Quality Technology & Quantitative Management, 3(2), 127-144.
[14] Ferrell, W. G., and Chhoker, A. (2002). "Design of economically optimal acceptance sampling plans with inspection error". Computers and Operations Research, 29, 1283-1300.
[15] Gan, F. F. (1995). "Joint monitoring of process mean and variance using exponentially weighted moving average control charts". Technometrics, 37, 446-453.
[16] Golhar, D. Y. (1987). "Determination of the best mean contents for a canning problem". Journal of Quality Technology, 19, 82-84.
[17] Hunter, W. G., and Kartha, C. P. (1977). "Determining the most profitable target value for a production process". Journal of Quality Technology, 9, 176-181.
[18] Kapur, K. C. (1987). "Quality loss function and inspection". Quality Control, Innovations in Quality: Concepts and Applications.
[19] Kapur, K. C., and Wang, D. J. (1987). "Economic design of specifications based on Taguchi’s concept of quality loss function". Proceeding of American Society of Mechanical Engineers.
[20] Lee, M. K., and Kim, G. S. (1994). "Determination of the optimal target values for a filling process when inspection is based on a correlation variable". International Journal of Production Economics, 37, 205-213.
[21] Lorenzen, T. J., and Vance, L. C. (1986). The economic design of control charts: a unified approach. Technometrics, 28(1), 3-10.
[22] Lucas, J. M., and Saccucci, M. S. (1990). "Average run lengths for exponentially weighted moving averages schemes using the Markov Chain approach". Journal of Quality Technology, 22, 154-162.
[23] Maghsoodloo, S., and Li, M. (2000). "Optimal asymmetric tolerance design". IIE Transactions, 32, 1127-1137.
[24] Mei, W. H., Case, K. E., and Schmidt, J. W. (1975). "Bias and impercision in variable acceptance sampling: effects and compensation". International Journal of Production Research, 13, 327-340.
[25] Menzefricke, E. (1984). "The effects of variability in inspection error". Journal of Quality Technology, 16, 131-135.
[26] Montgomery, D. C. (1985). Economic Design of X-bar Control Charts for Two Manufacturing Process Models. Naval Research Logistics Quarterly, 32, 631-646.
[27] Sheng (2012). "最小成本下, 規格及X-bar S管制圖之設計". Unpublished master thesis, Department of Statistics, NCCU.
[28] Stemann, D., and Weihs, C. (2001). "The EWMA-X-S control chart and its performance in the case of precise and imprecise data". Statistical Papers, 42, 207-223.
[29] Tang, K. (1987). "The effects of inspection error on a complete inspection plan". IIE Transactions, 19, 421-428.
[30] Tang, K. (1988). "Economic design of product specification for a complete inspection plan". International Journal of Production Research, 26(203-217).
[31] Tang, K., and Lo, J. (1993). "Determination of the process mean when inspection is based on a correlated variable". IIE Transactions, 25, 66-72.
[32] Tang, K., and Schneider, H. (1990). "Cost effectiveness of using a correlated variable in a complete inspection plan when inspection error is present". Naval Research Logistics Quarterly, 37, 893-904.
[33] Yang, S.F. (2013). "Using a new VSI EWMA average loss control chart to monitor changes in the difference between the process mean and target and/or the process variability". Journal of Mathematical Modelling. online publish.
描述 碩士
國立政治大學
統計研究所
100354014
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100354014
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 林裕景zh_TW
dc.creator (作者) 林裕景zh_TW
dc.date (日期) 2012en_US
dc.date.accessioned 1-Jul-2013 17:01:20 (UTC+8)-
dc.date.available 1-Jul-2013 17:01:20 (UTC+8)-
dc.date.issued (上傳時間) 1-Jul-2013 17:01:20 (UTC+8)-
dc.identifier (Other Identifiers) G0100354014en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58667-
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) 100354014zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 測量誤差在品質控制中是一個重要的議題，所以在本研究中考慮生產者的儀器具有測量誤差。當生產者的儀器具測量誤差被考慮時，我們假設生產者可採取完全的檢驗計畫或製成的控管，以保持產品的質量。我們透過比較各自的利潤選擇一個較好的品質控制政策。在完整的檢查計劃，對於不合格品我們考慮兩種方案，分別為完美的維修與以較低的價格銷售。於最大化利潤下，我們比較這兩種方案的利潤，以確定採取何種方案對生產者而言利潤會較大。
在本文中，我們也考慮一個中間商的角色。我們假定中間商與生產者的規格界限是相同的；而中間人購買的產品可能來自於生產者採取完美的維修或生產者採取以較低的價格銷售。在最大化中間商的利潤下，我們決定了中間商的規格界限，買入和賣出的價格。我們也比較這兩種方案下中間商的利潤以找出中間商應購買何種方案的商品能使其利潤最大。
在我們的分析中，我們發現，在製程中符合單位時間小生產量、高維修成本，高的不合格品成本，及高的售價時，那麼生產者應採取製程管制，否則生產者應採取完整檢驗才會使生產者具有較大的利潤。當中間商的儀器包含測量誤差時，中間商應購買的產品為來自於生產者採取完美的維修。		zh_TW
dc.description.abstract (摘要) Measurement error is an important issue in quality control, so in this study a producer instrument with measurement error is considered. When its instrument contains measurement error, we assume that a producer takes either complete inspection or on-line process control to maintain products quality. We then compare their respective profits to choose a better quality control policy. Also in the complete inspection plan we consider perfect repair and selling at a lower price are two actions for a producer to deal with nonconforming items. Under the maximizing profit model, we determine the optimal specification limits for the producer, and then compare the profit of these two actions to determine which action is better for producer to take.
In this article we also consider the act of a middleman. We assume that the specification limits of the middleman and producer are the same and the product that middleman bought may come from perfect repair action or selling at a lower price action. When maximizing the middleman’s profit, we determine the specification limits, buying and selling price of middleman, and we also compare the profit from these two actions to find out which action is better for the middleman.
In our analysis, we found that when process has a small production per unit time, a high repair cost, a high cost of nonconforming item, and a high sell price, then process control should be preferred by producer; otherwise the producer should take complete inspection. And to have a larger profit, middleman should buy products from producer who took the action of perfect repair when middleman’s instrument contains measurement error or middleman’s instrument contains no measurement error but producer’s instrument contains a small measurement error.		en_US
dc.description.tableofcontents CHAPTER 1. INTRODUCTION 1
1.1 Literature Review and Study Motivation 1
1.2 Research Method 4
CHAPTER 2. MAXIMIZE PRODUCER PROFIT UNDER INSTRUMENT WITH MEASUREMENT ERROR 6
2.1 Notations 7
2.2 Assumptions for Quality Variables 7
2.3 Complete Inspection and Adopting Two Actions for Observed Nonconforming Items 9
2.3.1 Perfect repair for observed nonconforming items 9
2.3.2 Taking sell low price action for observed nonconforming items. 23
2.4 Process Control Using Chart 40
2.4.1 Parameters notation 40
2.4.2 Establish chart. 41
2.4.3 Derivation of the profit model per unit time. 45
2.4.4 Determine the optimal design parameters and data analyses. 47
2.5 Comparing the Expected Profit Per Unit Time for Complete Inspection Plan and Process Control. 55
CHAPTER 3. DERIVE AND COMPARE THE MIDDLEMAN PROFITS PER ITEM UNDER PRODUCER TAKING TWO ACTIONS 62
3.1 Notations 62
3.2 Maximize the Profit Model to Determine the Optimal Specification Limits for Middleman under Producer Adopts Perfect Repair Action 63
3.2.1 Derivation of the profit model for middleman. 63
3.3 Maximize the Profit Model to Determine the Optimal Specification Limits for Middleman under Producer Adopts Sell Low Price Action. 83
3.3.1 Derivation of the profit model for middleman 83
3.3.2 Determine the optimal specification limits, middleman buying and selling price with Data analyses. 91
3.4 Compare Expected Profit per item for Middleman under Producer Take Different Actions. 102
3.4.1 Compare profits of middleman for middleman instrument without measurement error under producer’s two actions 102
3.4.2 Comparing the four cases expected profit of middleman for middleman instrument with measurement error. 105
CHAPTER 4. DERIVE THE MIDDLEMAN PROFIT MODEL WITH CONSIDERING ORDER QUANTITY UNDER PRODUCER TAKING TWO ACTIONS 110
4.1 Notations 110
4.2 Describe the Sell Price and Order Quantity Relationship among Producer, Middleman and Customer 110
4.3 Maximize the Profit Model to Determine the Optimal Specification Limits, Order Quantity, Buying and Selling Price for Middleman under Producer Adopting Perfect Repair Action. 111
4.3.1 Derivation of the profit model with order quantity for middleman. 111
4.3.2 Determine the optimal specification limits, middleman order quantity, buying and selling price for middleman with the data analyses. 115
4.3.3 Comparing the middleman ordered quantity and middleman profit for middleman instrument without and with measurement error under producer taking perfect repair action. 118
4.4 Maximize the Profit Model to Determine the Optimal Specification Limits, Order Quantity, Buying and Selling Price for Middleman under Producer Adopting Sell Low Price Action. 121
4.4.1 Derivation of the profit model with order quantity for middleman. 121
4.4.2 Determine the optimal specification limits, middleman order quantity, buying and selling price for middleman with the data analyses. 129
4.4.3 Comparing the middleman ordered quantity and middleman profit for middleman instrument with and without measurement error under producer taking sell low price action. 132
4.5 Compare Expected Profit per Week for Middleman under Producer Take Different Actions. 135
4.5.1 Comparing ordered quantity and expected profit of the middleman for middleman instrument without measurement error. 135
4.5.2 Comparing ordered quantity and expected profit of the middleman for middleman instrument with measurement error. 138
CHAPTER 5. SUMMARY AND FUTURE STUDY 143
REFERENCES 145
APPENDIXES 147
Appendix A. Derive the Distribution of 147
Appendix B. Calculate the Average Run Length 148		zh_TW
dc.format.extent 2198449 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/#G0100354014en_US
dc.subject (關鍵詞) 量測誤差zh_TW
dc.subject (關鍵詞) 完美的維修方案zh_TW
dc.subject (關鍵詞) 低價格銷售方案zh_TW
dc.subject (關鍵詞) 中間商zh_TW
dc.subject (關鍵詞) Measurement erroren_US
dc.subject (關鍵詞) Perfect repair actionen_US
dc.subject (關鍵詞) Sell low price actionen_US
dc.subject (關鍵詞) Middlemanen_US
dc.title (題名) 生產者與中間商利潤模式有量測誤差下規格之最適設計zh_TW
dc.title (題名) Optimal Design of Specification Limits under Profit Models with Measurement Errorsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Bennett, G. K., Case, K. E., and Schmidt, J. W. (1974). The economic effects of inspection errors on attribute sampling plan. Naval Research Logistics Quarterly, 21, 431-464.
[2] Biegel, J. (1974). "Inspection errors and sampling plans". AIIE Transactions, 6(431-464).
[3] Bisgaard, S., Hunter, W. G., and Pallesen, L. (1984). "Economic selection of quality of manufactured product". Technometrics, 26, 9-18.
[4] Case, K. E. (1980). "The P control chart under inspection error". Journal of Quality Technology, 12, 1-9.
[5] Chen, C. H. (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
[6] Chen., and Chung, K. J. (1994). "Inspection error effects on economic selection of target value for a production process". European Journal of Operational Research, 79, 311-324.
[7] Chen., and Chung, K. J. (1996). "Selection of the optimal precision level and target value for a production process: the lower-specification-limit case". IIE Transactions, 28, 979-985.
[8] Crowder, S. V., and Hamilton, M. D. (1992). "An EWMA for monitoring a process standard devation". Journal of Quality Technology, 24, 12-21.
[9] Dooris, A. L. (1977). "The effect of inspection error on the operation of a c-chart". AIIE Transactions, 9, 312-315.
[10] Duffuaa, S., and Siddiqui, A. W. (2003). "Process targeting with multi-class screening and measurement error". International Journal of Production Research, 41, 1373-1391.
[11] Duncan, A. (1956). "The economic design of X-bar chart used to maintain current control of aprocess". Journal of The American Statistical Association, 51, 228-242.
[12] Fathi, Y. (1990). "Producer-consumer tolerance". Journal of Quality Technology, 22, 138-145.
[13] Feng, and Kapur. (2006). Economic design of specifications for 100% inspection with imperfect measurement systems. Quality Technology & Quantitative Management, 3(2), 127-144.
[14] Ferrell, W. G., and Chhoker, A. (2002). "Design of economically optimal acceptance sampling plans with inspection error". Computers and Operations Research, 29, 1283-1300.
[15] Gan, F. F. (1995). "Joint monitoring of process mean and variance using exponentially weighted moving average control charts". Technometrics, 37, 446-453.
[16] Golhar, D. Y. (1987). "Determination of the best mean contents for a canning problem". Journal of Quality Technology, 19, 82-84.
[17] Hunter, W. G., and Kartha, C. P. (1977). "Determining the most profitable target value for a production process". Journal of Quality Technology, 9, 176-181.
[18] Kapur, K. C. (1987). "Quality loss function and inspection". Quality Control, Innovations in Quality: Concepts and Applications.
[19] Kapur, K. C., and Wang, D. J. (1987). "Economic design of specifications based on Taguchi’s concept of quality loss function". Proceeding of American Society of Mechanical Engineers.
[20] Lee, M. K., and Kim, G. S. (1994). "Determination of the optimal target values for a filling process when inspection is based on a correlation variable". International Journal of Production Economics, 37, 205-213.
[21] Lorenzen, T. J., and Vance, L. C. (1986). The economic design of control charts: a unified approach. Technometrics, 28(1), 3-10.
[22] Lucas, J. M., and Saccucci, M. S. (1990). "Average run lengths for exponentially weighted moving averages schemes using the Markov Chain approach". Journal of Quality Technology, 22, 154-162.
[23] Maghsoodloo, S., and Li, M. (2000). "Optimal asymmetric tolerance design". IIE Transactions, 32, 1127-1137.
[24] Mei, W. H., Case, K. E., and Schmidt, J. W. (1975). "Bias and impercision in variable acceptance sampling: effects and compensation". International Journal of Production Research, 13, 327-340.
[25] Menzefricke, E. (1984). "The effects of variability in inspection error". Journal of Quality Technology, 16, 131-135.
[26] Montgomery, D. C. (1985). Economic Design of X-bar Control Charts for Two Manufacturing Process Models. Naval Research Logistics Quarterly, 32, 631-646.
[27] Sheng (2012). "最小成本下, 規格及X-bar S管制圖之設計". Unpublished master thesis, Department of Statistics, NCCU.
[28] Stemann, D., and Weihs, C. (2001). "The EWMA-X-S control chart and its performance in the case of precise and imprecise data". Statistical Papers, 42, 207-223.
[29] Tang, K. (1987). "The effects of inspection error on a complete inspection plan". IIE Transactions, 19, 421-428.
[30] Tang, K. (1988). "Economic design of product specification for a complete inspection plan". International Journal of Production Research, 26(203-217).
[31] Tang, K., and Lo, J. (1993). "Determination of the process mean when inspection is based on a correlated variable". IIE Transactions, 25, 66-72.
[32] Tang, K., and Schneider, H. (1990). "Cost effectiveness of using a correlated variable in a complete inspection plan when inspection error is present". Naval Research Logistics Quarterly, 37, 893-904.
[33] Yang, S.F. (2013). "Using a new VSI EWMA average loss control chart to monitor changes in the difference between the process mean and target and/or the process variability". Journal of Mathematical Modelling. online publish.		zh_TW