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題名 具變動抽樣間隔的雙次抽樣損失管制圖之設計
沒英文名稱
作者 王嘉煒
貢獻者 楊素芬
王嘉煒
關鍵詞 管制圖
日期 2013
上傳時間 21-Jul-2014 15:37:04 (UTC+8)
摘要 本篇研究的目的為建立Optimal DS AL管制圖，並以ARL為績效的衡量指標，接著以R軟體的基因演算法決定使失控ARL最小化的管制界線。接著建立DSVSI EWMA AL管制圖，並以ATS為績效的衡量指標。當EWMA的權重 時，DSVSI EWMA AL管制圖則簡化為DSVSI AL管制圖，當固定抽樣間隔時，DSVSI EWMA AL管制圖則簡化為DS EWMA AL管制圖，當EWMA的權重 且抽樣間隔固定時，DSVSI EWMA AL管制圖則簡化為DS AL管制圖。最後以資料分析比較 DSVSI EWMA AL管制圖、DSVSI AL管制圖 、DS EWMA AL管制圖、Optimal DS AL管制圖、 DS AL管制圖 、 Optimal VSI AL管制圖(Yang 2013a) 、AL管制圖(Yang 2013)和DS X-bar and S管制圖(He and Grigoryan 2004)之失控的偵測績效。
參考文獻 陸、 參考文獻

Costa, A. F. (1998). Joint X-bar and R charts with variable parameters. IIE transactions, 30(6), 505-514.

Chen, G., and Cheng, S. W. (1998). Max chart: combining X-bar chart and S chart. Statistica Sinica, 8(1), 263-271.

Carot, V., Jabaloyes, J. M., and Carot, T. (2002). Combined double sampling and variable sampling interval X-bar chart. International Journal of Production Research,40(9), 2175-2186.

Daudin, J. J. (1992). Double Sampling X-bar Charts. Journal of Quality Technology , 24 78-87.

Farebrother, R. W. (1984). Algorithm AS 204: The distribution of a positive linear combination of χ 2 random variables. Applied Statistics, 332-339.

Grabov, P., and Ingman, D. (1996). Adaptive control limits for bivariate process monitoring. Journal of quality technology, 28(3), 320-330.

He, D., and Grigoryan, A. (2002). Construction of double sampling s‐control charts for agile manufacturing. Quality and reliability engineering international,18(4), 343-355.

He, D., and Grigoryan, A. (2006). Joint statistical design of double sampling X-bar and S charts. European Journal of Operational Research, 168(1), 122-142.

Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 419-426.

Liu, H., Tang, Y., and Zhang, H. H. (2009). A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. Computational Statistics & Data Analysis, 53(4), 853-856.

Lee, P. H., Chang, Y. C., and Torng, C. C. (2012). A design of S control charts with a combined double sampling and variable sampling interval scheme.Communications in Statistics-Theory and Methods, 41(1), 153-165.


Moschopoulos, P. G., and Canada, W. B. (1984). The distribution function of a linear combination of chi-squares. Computers & mathematics with applications,10(4), 383-386.

Patnaik, P. B. (1949). The non-central χ2-and F-distributions and their pplications. Biometrika, 36(1-2), 202-232.

Page, E. S. (1954). Continuous inspection schemes. Biometrika, 100-115.

Roberts, S. W. (1958). Properties of control chart zone tests. Bell System Technical Journal, 37(1), 83-114.

Reynolds, M. R., Amin, R. W., Arnold, J. C., and Nachlas, J. A. (1988). X-bar charts with variable sampling intervals. Technometrics, 30(2), 181-192.

Shewhart, W. A. (1931). Economic control of quality of manufactured product(Vol. 509). ASQ Quality Press.

Sullivan, J. H., and Woodall, W. H. (1996). A comparison of multivariate control charts for individual observations. Journal of Quality Technology, 28(4).

Spiring, F. A., and Cheng, S. W. (1998). An alternate variables control chart: the univariate and multivariate case. Statistica Sinica, 8(1), 273-287.

Wu, Z., and Tian, Y. (2006). Weighted-loss-function control charts. The International Journal of Advanced Manufacturing Technology, 31(1-2), 107-115.

Yang, S. F. (2013a). Using a Single Average Loss Control Chart to Monitor Process Mean and Variability. Communications in Statistics-Simulation and Computation, 42(7), 1549-1562.

Yang, S. F. (2013b). 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. Applied Mathematical Modelling, 37(16), 7973-7982.
描述 碩士
國立政治大學
統計研究所
101354022
102
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0101354022
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 王嘉煒zh_TW
dc.creator (作者) 王嘉煒zh_TW
dc.date (日期) 2013en_US
dc.date.accessioned 21-Jul-2014 15:37:04 (UTC+8)-
dc.date.available 21-Jul-2014 15:37:04 (UTC+8)-
dc.date.issued (上傳時間) 21-Jul-2014 15:37:04 (UTC+8)-
dc.identifier (Other Identifiers) G0101354022en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/67590-
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) 101354022zh_TW
dc.description (描述) 102zh_TW
dc.description.abstract (摘要) 本篇研究的目的為建立Optimal DS AL管制圖，並以ARL為績效的衡量指標，接著以R軟體的基因演算法決定使失控ARL最小化的管制界線。接著建立DSVSI EWMA AL管制圖，並以ATS為績效的衡量指標。當EWMA的權重 時，DSVSI EWMA AL管制圖則簡化為DSVSI AL管制圖，當固定抽樣間隔時，DSVSI EWMA AL管制圖則簡化為DS EWMA AL管制圖，當EWMA的權重 且抽樣間隔固定時，DSVSI EWMA AL管制圖則簡化為DS AL管制圖。最後以資料分析比較 DSVSI EWMA AL管制圖、DSVSI AL管制圖 、DS EWMA AL管制圖、Optimal DS AL管制圖、 DS AL管制圖 、 Optimal VSI AL管制圖(Yang 2013a) 、AL管制圖(Yang 2013)和DS X-bar and S管制圖(He and Grigoryan 2004)之失控的偵測績效。zh_TW
dc.description.tableofcontents 壹、 緒論 8
一、 前言 8
二、 研究動機 10
三、 研究目的與方法 10
貳、 DS AL管制圖的設計與績效衡量 11
一、 DS AL管制圖的追蹤統計量之分配 11
二、 DS AL管制圖的設計 14
三、 DS AL管制圖的績效衡量 16
四、 敏感度分析 20
參、 最適DS AL管制圖的設計與績效衡量 40
一、 設計最小ARL1下的DS AL管制圖 40
二、 最適DS AL管制圖和文獻上存在的相關管制圖之績效比較 42
肆、 DSVSI EWMA AL管制圖的設計與績效衡量 68
一、 DSVSI EWMA AL管制圖的追蹤統計量之分配與設計 68
二、 DSVSI EWMA AL管制圖的績效衡量 71
三、 敏感度分析 78
四、 DSVSI EWMA AL管制圖和其他相關管制圖節省績效比較 81
伍、 結論與建議 84
陸、 參考文獻 110		zh_TW
dc.format.extent 3024502 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/#G0101354022en_US
dc.subject (關鍵詞) 管制圖zh_TW
dc.title (題名) 具變動抽樣間隔的雙次抽樣損失管制圖之設計zh_TW
dc.title (題名) 沒英文名稱zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 陸、 參考文獻

Costa, A. F. (1998). Joint X-bar and R charts with variable parameters. IIE transactions, 30(6), 505-514.

Chen, G., and Cheng, S. W. (1998). Max chart: combining X-bar chart and S chart. Statistica Sinica, 8(1), 263-271.

Carot, V., Jabaloyes, J. M., and Carot, T. (2002). Combined double sampling and variable sampling interval X-bar chart. International Journal of Production Research,40(9), 2175-2186.

Daudin, J. J. (1992). Double Sampling X-bar Charts. Journal of Quality Technology , 24 78-87.

Farebrother, R. W. (1984). Algorithm AS 204: The distribution of a positive linear combination of χ 2 random variables. Applied Statistics, 332-339.

Grabov, P., and Ingman, D. (1996). Adaptive control limits for bivariate process monitoring. Journal of quality technology, 28(3), 320-330.

He, D., and Grigoryan, A. (2002). Construction of double sampling s‐control charts for agile manufacturing. Quality and reliability engineering international,18(4), 343-355.

He, D., and Grigoryan, A. (2006). Joint statistical design of double sampling X-bar and S charts. European Journal of Operational Research, 168(1), 122-142.

Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 419-426.

Liu, H., Tang, Y., and Zhang, H. H. (2009). A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. Computational Statistics & Data Analysis, 53(4), 853-856.

Lee, P. H., Chang, Y. C., and Torng, C. C. (2012). A design of S control charts with a combined double sampling and variable sampling interval scheme.Communications in Statistics-Theory and Methods, 41(1), 153-165.


Moschopoulos, P. G., and Canada, W. B. (1984). The distribution function of a linear combination of chi-squares. Computers & mathematics with applications,10(4), 383-386.

Patnaik, P. B. (1949). The non-central χ2-and F-distributions and their pplications. Biometrika, 36(1-2), 202-232.

Page, E. S. (1954). Continuous inspection schemes. Biometrika, 100-115.

Roberts, S. W. (1958). Properties of control chart zone tests. Bell System Technical Journal, 37(1), 83-114.

Reynolds, M. R., Amin, R. W., Arnold, J. C., and Nachlas, J. A. (1988). X-bar charts with variable sampling intervals. Technometrics, 30(2), 181-192.

Shewhart, W. A. (1931). Economic control of quality of manufactured product(Vol. 509). ASQ Quality Press.

Sullivan, J. H., and Woodall, W. H. (1996). A comparison of multivariate control charts for individual observations. Journal of Quality Technology, 28(4).

Spiring, F. A., and Cheng, S. W. (1998). An alternate variables control chart: the univariate and multivariate case. Statistica Sinica, 8(1), 273-287.

Wu, Z., and Tian, Y. (2006). Weighted-loss-function control charts. The International Journal of Advanced Manufacturing Technology, 31(1-2), 107-115.

Yang, S. F. (2013a). Using a Single Average Loss Control Chart to Monitor Process Mean and Variability. Communications in Statistics-Simulation and Computation, 42(7), 1549-1562.

Yang, S. F. (2013b). 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. Applied Mathematical Modelling, 37(16), 7973-7982.		zh_TW