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題名 考慮韋伯分配下兩個相依製程之管制
Process Control for Two Dependent Subprocess under Weibull Shock Model
作者 陳延宗
Chen, Yen-Tsung
貢獻者 楊素芬
Yang, Su-Fen
陳延宗
Chen, Yen-Tsung
關鍵詞 韋伯分配
選控圖
更新理論
Weibull distribution
cause-selecting chart
renewal theorem
日期 2000
上傳時間 31-Mar-2016 14:44:31 (UTC+8)
摘要 Today, most products are produced by several dependent subprocesses. This paper considers the economic-statistical process control for two dependent subprocesses with two assignable causes following Weibull shock distributions. We construct the individual X control chart to monitor the in-coming quality produced by previous process, and use the cause-selecting control chart to monitor the specific quality produced by current process. By using the charts, we can effectively and economically distinguish which subprocess is out of control. The renewal theorem approach is extended to construct the cost model for our proposed control charts, and the successive quadratic programming algorithm and a finite difference gradient method in the Fortran IMSL subroutine (dnconf) is used to determine the optimal design parameters of the proposed control charts. Finally, we give an example to show how to construct and apply the proposed control charts. Furthermore, the sensitivity analysis illustrates the effects of cost and process parameters on the optimal design parameters and the minimal expected cost per unit time for the proposed control charts.
參考文獻 Banerjee, P. and Rahim, M. (1987), ”The Economic Design of Control Charts : A Renewal Theory Approach”, Engineering Optimization, Vol. 12, pp. 63-73.
Banerjee, P. K. and Rahim, M. A. (1988). “Economic Design of Control Charts under Weibull Shock Model”,Technometrics, Vol.30, pp. 407-414.
Chen, G. and Kapur, k. (1989). “Quality Evaluation System Using Loss Function”, International Industrial Engineering Conference Societies’ Manufacturing and Productivity Symposium Proceeding, pp.363-8.
Chung, K. (1991), “Economic Design of Attribute Control Charts For Multiple Assignable Causes”, Optimization, 22, 5, pp.775-786.
Collani, V. and Sheil, J. (1989), “An Approach to Controlling Process Variability”, Journal of Quality Technology, Vol.21, pp. 87-96.
Duncan, A.(1956), “The Economic Design of Chart Used to Maintain Current Control of A Process”, American Statistical Association Journal, Vol. 51, pp. 228-42.
Duncan, A.(1971), “The Economic Design of Charts When There is A Multiplicity of Assignable Causes”, American Statistical Association Journal, Vol. 66, No.33, pp.107-121.
Elsayed, E. and Chen, A.(1994), “ An Economic Design of Control Chart Using Quadratic Loss Function “, International Journal of Production Research, Vol. 32, pp.873-37.
Hu, P. W. (1984), "Economic Design of an X-bar Control Chart Under Non-Poission Process Shift," Abstract, TIMS/ORSA Joint National meeting, San Francisco, May 14-16, p.87.
IMSL Library (1989), User’s Manual Math/Library, Fortran Subroutines, IMSL, Inc.
Jones, L. and Case, K. (1981), “Economic Design of An X- and R-Chart”, AIIE Transactions. Vol. 13, pp. 182-95.
Kacker. ,R. (1986).”Taguchi’s Quality Philosophy: Analysis and Commentary”, Quality Progress, December, pp. 21-9.
Koo, T. and Lin, L. (1992), “Economic Design of X-bar Chart When Taguchi’s Loss Function is Considered”, Proceedings of Asian Quality Control Symposium, South Korea. pp. 166-78.
Rahim, M. (1989). “ Determination of Optimal Design Parameters of Joint and R Charts”, Journal of Quality Technology, Vol. 21, pp. 65-70.
Rahim, M., Lashkari, R. and Banerjee, P. (1988), “Joint Economic Design of Mean and Variance Control Charts”, Engineering Optimization, Vol. 14, pp. 65-78.
Shewhart, W. (1931), Economic Control of Quality of Manufactured Product, D. Van Nostrand Company, Inc.
Saniga, E. (1977), “ Joint Economically Optimal Design of X-and R-Control Charts”, Management science, Vol. 24, pp. 420-31.
Saniga, E. (1979), “Statistical Control-Chart Designs with an Application to and R Control Charts”, Management science, Vol. 31, pp.313-20.
Saniga, E. and Montgomery, D. (1981), “Economically Quality Control Policies for A Single Cause”, AIIE Transactions, Vol. 13, pp. 258-64.
Tagaras, G. and Lee, H (1988), “Economic Design of Control Charts with Different Control Limits for Different Assignable Causes”, Management Science, Vol. 34, No. 11, pp. 1347-66.
Taguchi, G.(1984), “The Role of Metrological Control for Quality Control”, Proceedings of the International Symposium on Metrology for quality control in production. Pp. 1-7.
Taguchi, G., Elsayed, E. and Hsiang, T. (1989), Quality Engineering in Production Systems, McGraw-Hill, New York, NY.
Wade, R. and Woodall, W. (1993), “A Review and Analysis of Cause-Selecting Control Charts”, Journal of Quality Technology, Vol. 25, pp.161-9.
Woodall, W. (1986), “Weaknesses of The Economic Design of Control Charts”, Technometrics, Vol. 28, pp. 408-9.
Woodall, W. (1987), “Conflicts between Deming’s Philosophy and The Economic Design of Control Charts”, Frontiers in Statistical Quality Control, Vol. 3, pp. 242-8.
Yang, C. (1997),”The Economic Design of Simple Cause-Selecting Control Charts”, Journal and Newsletter for Quality and Reliability, Vol.12, No.4, pp. 215-225.
Yang, S. (1997), ”The Economic Design of Control Charts When There are Dependent Process Steps”, International Journal of Quality & Reliability Management, Vol. 14, No. 6, pp.606-615.
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.
Yang, S. (1998), “Economic Statistical Design of S Control Charts Using Taguchi Loss Function”, International Journal of Quality & Reliability Management, Vol. 15, No. 3, pp. 259-272.
Zhang, G. (1984), “A New Type of Control Charts and a theory of Diagnosis with Control Charts”, World Quality Congress Transactions, American Society for Quality Control, Milwaukee, WI, pp.75-85.
描述 碩士
國立政治大學
統計學系
87354009
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001933
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.advisor Yang, Su-Fenen_US
dc.contributor.author (Authors) 陳延宗zh_TW
dc.contributor.author (Authors) Chen, Yen-Tsungen_US
dc.creator (作者) 陳延宗zh_TW
dc.creator (作者) Chen, Yen-Tsungen_US
dc.date (日期) 2000en_US
dc.date.accessioned 31-Mar-2016 14:44:31 (UTC+8)-
dc.date.available 31-Mar-2016 14:44:31 (UTC+8)-
dc.date.issued (上傳時間) 31-Mar-2016 14:44:31 (UTC+8)-
dc.identifier (Other Identifiers) A2002001933en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/83240-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 87354009zh_TW
dc.description.abstract (摘要) Today, most products are produced by several dependent subprocesses. This paper considers the economic-statistical process control for two dependent subprocesses with two assignable causes following Weibull shock distributions. We construct the individual X control chart to monitor the in-coming quality produced by previous process, and use the cause-selecting control chart to monitor the specific quality produced by current process. By using the charts, we can effectively and economically distinguish which subprocess is out of control. The renewal theorem approach is extended to construct the cost model for our proposed control charts, and the successive quadratic programming algorithm and a finite difference gradient method in the Fortran IMSL subroutine (dnconf) is used to determine the optimal design parameters of the proposed control charts. Finally, we give an example to show how to construct and apply the proposed control charts. Furthermore, the sensitivity analysis illustrates the effects of cost and process parameters on the optimal design parameters and the minimal expected cost per unit time for the proposed control charts.en_US
dc.description.tableofcontents 封面頁
證明書
致謝詞
論文摘要
目錄
表目錄
圖目錄
1. Introduction
2. The Process Model
2.1 Assumptions and Notation
2.2 The Relation between X and Y
2.3 Individual X Control Chart and Cause-Selecting Control Chart
3. The Cost Model
3.1 Type I and Type II Error Probabilities
3.2 The Asymmetric Loss Function
3.3 The Expected Cycle Length
3.4 The Expected Cycle Cost
3.5 Determination of the Optimal Design Parameters for the Proposed Control Charts
4. An Example and Sensitivity Analysis
4.1 An Example
4.2 Sensitivity Analysis
5. Conclusions and Suggestions
6. References
Appendix
Appendix I
Appendix II
Appendix III
Appendix IV
Appendix V		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001933en_US
dc.subject (關鍵詞) 韋伯分配zh_TW
dc.subject (關鍵詞) 選控圖zh_TW
dc.subject (關鍵詞) 更新理論zh_TW
dc.subject (關鍵詞) Weibull distributionen_US
dc.subject (關鍵詞) cause-selecting charten_US
dc.subject (關鍵詞) renewal theoremen_US
dc.title (題名) 考慮韋伯分配下兩個相依製程之管制zh_TW
dc.title (題名) Process Control for Two Dependent Subprocess under Weibull Shock Modelen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Banerjee, P. and Rahim, M. (1987), ”The Economic Design of Control Charts : A Renewal Theory Approach”, Engineering Optimization, Vol. 12, pp. 63-73.
Banerjee, P. K. and Rahim, M. A. (1988). “Economic Design of Control Charts under Weibull Shock Model”,Technometrics, Vol.30, pp. 407-414.
Chen, G. and Kapur, k. (1989). “Quality Evaluation System Using Loss Function”, International Industrial Engineering Conference Societies’ Manufacturing and Productivity Symposium Proceeding, pp.363-8.
Chung, K. (1991), “Economic Design of Attribute Control Charts For Multiple Assignable Causes”, Optimization, 22, 5, pp.775-786.
Collani, V. and Sheil, J. (1989), “An Approach to Controlling Process Variability”, Journal of Quality Technology, Vol.21, pp. 87-96.
Duncan, A.(1956), “The Economic Design of Chart Used to Maintain Current Control of A Process”, American Statistical Association Journal, Vol. 51, pp. 228-42.
Duncan, A.(1971), “The Economic Design of Charts When There is A Multiplicity of Assignable Causes”, American Statistical Association Journal, Vol. 66, No.33, pp.107-121.
Elsayed, E. and Chen, A.(1994), “ An Economic Design of Control Chart Using Quadratic Loss Function “, International Journal of Production Research, Vol. 32, pp.873-37.
Hu, P. W. (1984), "Economic Design of an X-bar Control Chart Under Non-Poission Process Shift," Abstract, TIMS/ORSA Joint National meeting, San Francisco, May 14-16, p.87.
IMSL Library (1989), User’s Manual Math/Library, Fortran Subroutines, IMSL, Inc.
Jones, L. and Case, K. (1981), “Economic Design of An X- and R-Chart”, AIIE Transactions. Vol. 13, pp. 182-95.
Kacker. ,R. (1986).”Taguchi’s Quality Philosophy: Analysis and Commentary”, Quality Progress, December, pp. 21-9.
Koo, T. and Lin, L. (1992), “Economic Design of X-bar Chart When Taguchi’s Loss Function is Considered”, Proceedings of Asian Quality Control Symposium, South Korea. pp. 166-78.
Rahim, M. (1989). “ Determination of Optimal Design Parameters of Joint and R Charts”, Journal of Quality Technology, Vol. 21, pp. 65-70.
Rahim, M., Lashkari, R. and Banerjee, P. (1988), “Joint Economic Design of Mean and Variance Control Charts”, Engineering Optimization, Vol. 14, pp. 65-78.
Shewhart, W. (1931), Economic Control of Quality of Manufactured Product, D. Van Nostrand Company, Inc.
Saniga, E. (1977), “ Joint Economically Optimal Design of X-and R-Control Charts”, Management science, Vol. 24, pp. 420-31.
Saniga, E. (1979), “Statistical Control-Chart Designs with an Application to and R Control Charts”, Management science, Vol. 31, pp.313-20.
Saniga, E. and Montgomery, D. (1981), “Economically Quality Control Policies for A Single Cause”, AIIE Transactions, Vol. 13, pp. 258-64.
Tagaras, G. and Lee, H (1988), “Economic Design of Control Charts with Different Control Limits for Different Assignable Causes”, Management Science, Vol. 34, No. 11, pp. 1347-66.
Taguchi, G.(1984), “The Role of Metrological Control for Quality Control”, Proceedings of the International Symposium on Metrology for quality control in production. Pp. 1-7.
Taguchi, G., Elsayed, E. and Hsiang, T. (1989), Quality Engineering in Production Systems, McGraw-Hill, New York, NY.
Wade, R. and Woodall, W. (1993), “A Review and Analysis of Cause-Selecting Control Charts”, Journal of Quality Technology, Vol. 25, pp.161-9.
Woodall, W. (1986), “Weaknesses of The Economic Design of Control Charts”, Technometrics, Vol. 28, pp. 408-9.
Woodall, W. (1987), “Conflicts between Deming’s Philosophy and The Economic Design of Control Charts”, Frontiers in Statistical Quality Control, Vol. 3, pp. 242-8.
Yang, C. (1997),”The Economic Design of Simple Cause-Selecting Control Charts”, Journal and Newsletter for Quality and Reliability, Vol.12, No.4, pp. 215-225.
Yang, S. (1997), ”The Economic Design of Control Charts When There are Dependent Process Steps”, International Journal of Quality & Reliability Management, Vol. 14, No. 6, pp.606-615.
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.
Yang, S. (1998), “Economic Statistical Design of S Control Charts Using Taguchi Loss Function”, International Journal of Quality & Reliability Management, Vol. 15, No. 3, pp. 259-272.
Zhang, G. (1984), “A New Type of Control Charts and a theory of Diagnosis with Control Charts”, World Quality Congress Transactions, American Society for Quality Control, Milwaukee, WI, pp.75-85.		zh_TW