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題名 動態機率管制界線的二項累積和管制圖的設計
Design of Binomial CUSUM Charts with Dynamic Probability Control Limits
作者 卓緯倫
Cho, Wei Lun
貢獻者 楊素芬
Yang, Su Fen
卓緯倫
Cho, Wei Lun
關鍵詞 不合格率
累積和
積分方程式
動態管制界線
快速起始反應
高良率製程
統計製程管制
Fraction Nonconforming
Cumulative sum
Integral equation
dynamic control limits
fast initial response
high yield process
statistical process control
日期 2015
上傳時間 27-Jul-2015 11:21:16 (UTC+8)
摘要 傳統的二項累積和(CUSUM)管制圖是監測不合格率變化的有效工具。在本文中，我們考慮了俱有機率管制界線的二項CUSUM管制圖的設計，旨在控制每一期的條件誤報率達到所需的值。與固定的管制界線相比，機率管制界線將會是動態的，且更一般化、更能適應各種複雜的實際情況。在本文中，我們著重在機率管制界線的決定。藉由積分方程式法的發展，以促成動態二項加權CUSUM管制圖的設計與分析。俱有機率管制界線或固定管制界線的二項加權CUSUM管制圖與是否俱有快速起始反應特性的管制圖皆進行了比較。此外，在高良率的情境下，我們互相比較俱有機率管制界線與固定管制界線的二項加權CUSUM管制圖在製程失控時的偵測力表現。舉了一個例子來說明該如何應用所提出的管制圖。比較的結果顯示，動態界線的管制圖優於固定管制界線的管制圖，且在高良率的情況下，若樣本數越大，對動態管制界線的管制圖越有利。
The conventional binomial CUSUM chart is an efficient tool for monitoring changes in fraction nonconforming. In this paper, we consider the design of Binomial CUSUM charts with probability control limits aimed at controlling the condi- tional false alarm rate at the desired value at each time step. The resulting control limits would be dynamic, which are more general and capable of accommodating more complex situations in practice as compared to the use of a constant control limit. In this paper, We focus on the determination of the probability control limits. An integral equation approach is developed to facilitate the design and analysis of the binomial WCUSUM control chart with probability control limits. The performance of the binomial WCUSUM charts with probability and constant control limits and the binomial WCUSUM charts with and without the fast initial response feature are compared. Besides, we compared the out-of-control detection perfromance of the binomial WCUSUM charts with probability and constant control limits for high yield process. An example is used to illustrate the application of the proposed control chart. Our comparisons show that the binomial WCUSUM chart with probability control limits generally outperforms the WCUSUM chart with constant control limits, and the conventional binomial CUSUM control chart with a constant control limit for high yield process when the sample size is large.
參考文獻 [1] Bourke, P. D. (1991). ”Detecting a Shift in Fraction Non-conforming Using Run-Length Control Charts with 100% Inspection”. Journal of Quality Technology 23(3), pp. 225-238.
[2] Bourke, P. D. (1992). ”Performance of Cumulative Sum Schemes for Monitor- ing Low Count-level Processes”. Metrika 39, pp. 365-384.
[3] Bourke, P. D. (2001). ”Sample Size and the Binomial CUSUM Control Chart: the Case of 100% Inspection”. Metrika 53, pp. 51-70.
[4] Box, G. E. P. and Ramirez, J. G. (1992). ”Cumulative Score Charts”. Quality and Reliability Engineering International 8(1), pp. 17-27.
[5] Calvin, T. W. (1987). ”Quality control techniques for ’zero-defects’”. Components, Hybrids and Manufacturing Technology 6, pp. 323-328.
[6] Chan, L. Y.; Xie, M.; and Goh, T. N. (2000). ”Cumulative Quantity Control Charts for Monitoring Production Processes”. International Journal of Production Research 38, pp. 397- 408.
[7] Chang, T. C. and Gan, F. F. (2001). ”Cumulative Sum Charts for High Yield Processes”. Statistica Sinica 11, pp. 791-805.
[8] Duran, R .I. and Albin, S. L. (2009). ”Monitoring a Fraction with Easy and Reliable Settings of the False Alarm Rate”. Quality and Reliability Engineering International 25(8), pp. 1029- 1043.
[9] Gan, F. F. (1990). ”Monitoring Observations Generated from a Binomial Distri- bution Using Modified Exponentially Weighted Moving Average Control Chart”. Journal of Statistical Computation and Simulation 37(1), pp. 45-60.
[10] Gan, F. F. (1993). ”An Optimal Design of CUSUM Control Charts for Binomial Counts”. Journal of Applied Statistics 20(4), pp. 445-460.
[11] Goh, T. N. (1987). ”A control chart for very high yield processes”. Quality Assurance 13, pp. 18-22.
[12] Haridy, S.; Wu, Z.; Yu, F. J.; and Shamsuzzaman, M. (2013). ”An Optimisation Design of the Combined n p-CUSUM Scheme for Attributes”. European Journal of Industrial Engineering 7(1), pp. 16-37.
[13] Huang, W.; Shu, L.; Woodall, W. H.; and Tsui, K. L. (2014). ”CUSUM Procedures with Probability Control Limits for Monitoring Processes with Variable Sample Sizes”.
[14] Khoo, M. B. C. (2004). ”A Moving Average Control Chart for Monitoring the Fraction Non-conforming”. Quality and Reliability Engineering International 20(6), pp. 617-635.
[15] Jiang, W.; Shu, L.; and Tsui, K.-L. (2011). ”Weighted CUSUM Control Charts for Moni- toring Inhomogeneous Poisson Processes with Varying Sample Sizes”. Journal of Quality Tech- nology 43(4), pp. 346-362.
[16] Lucas, J. M. (1989). ”Control Schemes for Low Count Levels”. Journal of Quality Tech- nology 21(3), pp. 199-201.
[17] Lucas, J. M., and Crosier, R. B. (1982). ”Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM a Head Start”. Technometrics 24(3), pp. 199-205.
[18] Lucas, J. M., and Saccucci, M. S. (1990). ”Exponentially Weighted Moving Average Con- trol Schemes: Properties and Enhancements”. Technometrics 32(1), pp. 1-12.
[19] Luceno, A. and Puig-Pey, J. (2000). ”Evaluationoftherun-length probability distribution for CUSUM charts: assessing chart performance”. Technometrics 42(4), pp. 411-416.
[20] Margavio, T. M.; Conerly, M. D.; Woodall, W. H.; and Drake, L. G. (1995). ”Alarm Rates for Quality Control Charts”. Statistics & Probability Letters 24(3), pp. 219-224.
[21] McCool, J. I. and Motley, T. J. (1998). ”Control Charts applicable when the fraction non- conforming is small”. Journal of Quality Technology 30, pp. 240-247.
[22] Mei, Y.; Han, S. W.; and Tsui, K-L. (2011). ”Early Detection of a Change in Poisson Rate after Accounting for Population Size Effects”. Statistica Sinica 21, pp. 597-624.
[23] Montgomery, D. C. (2009). Introduction to Statistical Quality Control, 7th Edition. Hobo- ken, NJ: John Wiley & Sons, Inc.
[24] Mousavi, S., and Reynolds, M.R., Jr. (2009). ”A CUSUM Chart for Monitoring a Pro- portion with Autocorrelated Binary Observations”. Journal of Quality Technology 41(4), pp. 401-414.
[25] Nelson, L. S. (1994). ”A control chart for parts-per-million nonconforming items”. Journal of Quality Technology, 26, pp. 239-240.
[26] Page, E. S. (1954). ”Continuous Inspection Schemes”. Biometrika 41, pp. 100-115.
[27] Pan, E. S.; Jin, Y.; Wang, S. Y.; and Cang, T. (2012). ”An Integrated EPQ Model based on a Control Chart for an Imperfect Production Process”. nternational Journal of Production Research 50(23), pp. 6999-7001.
[28] Perry, M. B. and Pignatiello, J. J. (2007). ”Change Point Estima- tion for Monotonically Changing Poisson Rates in SPC”. International Journal of Production Research 45(8), pp. 1791-1813.
[29] Perry, M. B. and Pignatiello, J. J. (2011). ”Estimating the Time of Step Change with Poisson CUSUM and EWMA Control Charts”. International Journal of Production Research 49(10), pp. 2857-2871.
[30] Quesenberry, C. P. (1991). ”SPC Q Charts for a Binomial Parameter p: Short or Long Runs”. Journal of Quality Technology 23(3), pp. 239-246.
[31] Quesenberry, C. P. (1995). ”Geometric Q charts for high quality pro- cesses”. Journal of Quality Technology 27(4), pp. 304-315.
[32] Quesenberry, C. P. (1995). ”On Properties of Binomial Q Charts for Attributes”. Journal of Quality Technology 27(3), pp. 204-213.
[33] Radaelli, G. (1994). ”Poisson and Negative Binomial Dynamics for Counted Data under CUSUM-type Charts”. Journal of Applied Statistics 21(5), pp. 347-356.
[34] Reynolds, M. R., Jr. and Stoumbos, Z. G. (1999). ”A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously”. Journal of Quality Technology 31(1), pp. 87-108. [35] Reynolds, M. R., Jr. and Stoumbos, Z.G. (2000). ”A General Approach to Modeling CUSUM Charts for a Proportion”. IIE Transactions 32(6), pp. 515-535.
[36] Saniga, E. M.; Davis, D. J.; and Lucas, J. M. (2009). ”Using Shewhart and CUSUM Charts for Diagnosis with Count data in a Vendor Certification Study”. Journal of Quality Technology 41(3), pp. 217-227.
[37] Sego, L. H.; Woodall, W. H.; and Reynolds, M. R. (2008). ”A Comparison of Surveillance Methods for Small Incidence Rates”. Statistics in Medicine 27(8), pp. 1225-1247.
[38] Shu, L.; Jiang, W.; and Tsui, K. L. (2008). ”A Weighted Cusum Chart for Detecting Pat- terned Mean Shifts”. Journal of Quality Technology 40(2), pp. 194-213.
[39] Shu, L.; Jiang, W.; and Tsui, K. L. (2011). ”A Comparison of Weighted CUSUM Procedures that Account for Monotone Changes in Population Size”. Statistics in Medicine 30(7), pp. 725- 741.
[40] Szarka, J. L. and Woodall, W. H. (2011). ”A Review and Perspec- tive on Surveillance of Bernoulli Processes”. Quality and Reliability Engineering Interna- tional 27(8), pp. 735-752. [41] Woodall, W. H. (1983). ”The distribution of the run length of one-sided CUSUM procedures for continuous random variables”. Technometrics 25(3), pp. 295-301.
[42] Woodall, W. H. (1997). ”ControlChartsbasedonAttributeData:Bibliography and Review”. Journal of Quality Technology 29, pp. 172-183.
[43] Wu, Z. and Jiao, J. X. (2008). ”A Control Chart for Monitoring Process Mean Based on Attribute Inspection”. International Journal of Production Research 46, pp. 4331-4347.
[44] Wu, Z.; Jiao, J. X.; and Liu, Y. (2008). ”A Binomial CUSUM Chart for Detecting Large Shifts in Fraction Nonconforming”. Journal of Applied Statistics 35(11), pp. 1267-1276.
[45] Wu, Z.; Yeo, S. H.; and Spedding, T. A. (2001). ”A Synthetic Control Chart for Detecting Fraction Nonconforming Increases”. Journal of Quality Technology 33(1), pp. 104-111.
[46] Yashchin, E. (1989). ”Weighted Cumulative Sum Technique”. Technometrics 31(3), pp. 321-338.
[47] Yashchin, E. (1993). ”Statistical Control Schemes: Methods, Applications and Generaliza- tions”. International Statistical Review 61(1), pp. 41-66.
[48] Yeha, A. B.; Mcgratha, R. N.; Sembowerb, M. A.; and Shen, Q. (2008). ”EWMA Control Charts for Monitoring High-yield Processes based on Nontransformed Observations”. Interna- tional Journal of Production Research 46(20), pp. 5679-5699.
[49] Zhou, Q.; Huang, W.; and Shu, L. (2014). ”A Comparison of Weighted CUSUM Proce- dures for Monitoring Process Proportions with Varying Sample Sizes”. International Journal of Production Research 52(11), pp. 3225-3238.
描述 碩士
國立政治大學
統計研究所
102354006
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102354006
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.advisor Yang, Su Fenen_US
dc.contributor.author (Authors) 卓緯倫zh_TW
dc.contributor.author (Authors) Cho, Wei Lunen_US
dc.creator (作者) 卓緯倫zh_TW
dc.creator (作者) Cho, Wei Lunen_US
dc.date (日期) 2015en_US
dc.date.accessioned 27-Jul-2015 11:21:16 (UTC+8)-
dc.date.available 27-Jul-2015 11:21:16 (UTC+8)-
dc.date.issued (上傳時間) 27-Jul-2015 11:21:16 (UTC+8)-
dc.identifier (Other Identifiers) G0102354006en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/76857-
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) 102354006zh_TW
dc.description.abstract (摘要) 傳統的二項累積和(CUSUM)管制圖是監測不合格率變化的有效工具。在本文中，我們考慮了俱有機率管制界線的二項CUSUM管制圖的設計，旨在控制每一期的條件誤報率達到所需的值。與固定的管制界線相比，機率管制界線將會是動態的，且更一般化、更能適應各種複雜的實際情況。在本文中，我們著重在機率管制界線的決定。藉由積分方程式法的發展，以促成動態二項加權CUSUM管制圖的設計與分析。俱有機率管制界線或固定管制界線的二項加權CUSUM管制圖與是否俱有快速起始反應特性的管制圖皆進行了比較。此外，在高良率的情境下，我們互相比較俱有機率管制界線與固定管制界線的二項加權CUSUM管制圖在製程失控時的偵測力表現。舉了一個例子來說明該如何應用所提出的管制圖。比較的結果顯示，動態界線的管制圖優於固定管制界線的管制圖，且在高良率的情況下，若樣本數越大，對動態管制界線的管制圖越有利。zh_TW
dc.description.abstract (摘要) The conventional binomial CUSUM chart is an efficient tool for monitoring changes in fraction nonconforming. In this paper, we consider the design of Binomial CUSUM charts with probability control limits aimed at controlling the condi- tional false alarm rate at the desired value at each time step. The resulting control limits would be dynamic, which are more general and capable of accommodating more complex situations in practice as compared to the use of a constant control limit. In this paper, We focus on the determination of the probability control limits. An integral equation approach is developed to facilitate the design and analysis of the binomial WCUSUM control chart with probability control limits. The performance of the binomial WCUSUM charts with probability and constant control limits and the binomial WCUSUM charts with and without the fast initial response feature are compared. Besides, we compared the out-of-control detection perfromance of the binomial WCUSUM charts with probability and constant control limits for high yield process. An example is used to illustrate the application of the proposed control chart. Our comparisons show that the binomial WCUSUM chart with probability control limits generally outperforms the WCUSUM chart with constant control limits, and the conventional binomial CUSUM control chart with a constant control limit for high yield process when the sample size is large.en_US
dc.description.tableofcontents Chapter 1 Introduction 1
Chapter 2 The CUSUM Chart with Probability Control Limits 4
Chapter 3 Determination of the Probability Control Limits of the WCM Chart 7
Chapter 4 Computation of the Out-of-Control ARL of the WCM Chart with Probability Control Limits 12
Chapter 5 Performance Comparison between the proposed WCM Chart and WCY Chart 14
Section 5.1 Performance Comparison of Dynamic WCM Chart and WCY charts with constant control limits 15
Section 5.2 Performance Comparison of the WCM and WCY charts with/without FIR feature 19
Chapter 6 Performance Comparison among CUSUM Charts for High Yield Process 23
Chapter 7 An illustrative example 27
Chapter 8 Conclusion 30
Appendix 32
Bibliography 35		zh_TW
dc.format.extent 370814 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102354006en_US
dc.subject (關鍵詞) 不合格率zh_TW
dc.subject (關鍵詞) 累積和zh_TW
dc.subject (關鍵詞) 積分方程式zh_TW
dc.subject (關鍵詞) 動態管制界線zh_TW
dc.subject (關鍵詞) 快速起始反應zh_TW
dc.subject (關鍵詞) 高良率製程zh_TW
dc.subject (關鍵詞) 統計製程管制zh_TW
dc.subject (關鍵詞) Fraction Nonconformingen_US
dc.subject (關鍵詞) Cumulative sumen_US
dc.subject (關鍵詞) Integral equationen_US
dc.subject (關鍵詞) dynamic control limitsen_US
dc.subject (關鍵詞) fast initial responseen_US
dc.subject (關鍵詞) high yield processen_US
dc.subject (關鍵詞) statistical process controlen_US
dc.title (題名) 動態機率管制界線的二項累積和管制圖的設計zh_TW
dc.title (題名) Design of Binomial CUSUM Charts with Dynamic Probability Control Limitsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Bourke, P. D. (1991). ”Detecting a Shift in Fraction Non-conforming Using Run-Length Control Charts with 100% Inspection”. Journal of Quality Technology 23(3), pp. 225-238.
[2] Bourke, P. D. (1992). ”Performance of Cumulative Sum Schemes for Monitor- ing Low Count-level Processes”. Metrika 39, pp. 365-384.
[3] Bourke, P. D. (2001). ”Sample Size and the Binomial CUSUM Control Chart: the Case of 100% Inspection”. Metrika 53, pp. 51-70.
[4] Box, G. E. P. and Ramirez, J. G. (1992). ”Cumulative Score Charts”. Quality and Reliability Engineering International 8(1), pp. 17-27.
[5] Calvin, T. W. (1987). ”Quality control techniques for ’zero-defects’”. Components, Hybrids and Manufacturing Technology 6, pp. 323-328.
[6] Chan, L. Y.; Xie, M.; and Goh, T. N. (2000). ”Cumulative Quantity Control Charts for Monitoring Production Processes”. International Journal of Production Research 38, pp. 397- 408.
[7] Chang, T. C. and Gan, F. F. (2001). ”Cumulative Sum Charts for High Yield Processes”. Statistica Sinica 11, pp. 791-805.
[8] Duran, R .I. and Albin, S. L. (2009). ”Monitoring a Fraction with Easy and Reliable Settings of the False Alarm Rate”. Quality and Reliability Engineering International 25(8), pp. 1029- 1043.
[9] Gan, F. F. (1990). ”Monitoring Observations Generated from a Binomial Distri- bution Using Modified Exponentially Weighted Moving Average Control Chart”. Journal of Statistical Computation and Simulation 37(1), pp. 45-60.
[10] Gan, F. F. (1993). ”An Optimal Design of CUSUM Control Charts for Binomial Counts”. Journal of Applied Statistics 20(4), pp. 445-460.
[11] Goh, T. N. (1987). ”A control chart for very high yield processes”. Quality Assurance 13, pp. 18-22.
[12] Haridy, S.; Wu, Z.; Yu, F. J.; and Shamsuzzaman, M. (2013). ”An Optimisation Design of the Combined n p-CUSUM Scheme for Attributes”. European Journal of Industrial Engineering 7(1), pp. 16-37.
[13] Huang, W.; Shu, L.; Woodall, W. H.; and Tsui, K. L. (2014). ”CUSUM Procedures with Probability Control Limits for Monitoring Processes with Variable Sample Sizes”.
[14] Khoo, M. B. C. (2004). ”A Moving Average Control Chart for Monitoring the Fraction Non-conforming”. Quality and Reliability Engineering International 20(6), pp. 617-635.
[15] Jiang, W.; Shu, L.; and Tsui, K.-L. (2011). ”Weighted CUSUM Control Charts for Moni- toring Inhomogeneous Poisson Processes with Varying Sample Sizes”. Journal of Quality Tech- nology 43(4), pp. 346-362.
[16] Lucas, J. M. (1989). ”Control Schemes for Low Count Levels”. Journal of Quality Tech- nology 21(3), pp. 199-201.
[17] Lucas, J. M., and Crosier, R. B. (1982). ”Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM a Head Start”. Technometrics 24(3), pp. 199-205.
[18] Lucas, J. M., and Saccucci, M. S. (1990). ”Exponentially Weighted Moving Average Con- trol Schemes: Properties and Enhancements”. Technometrics 32(1), pp. 1-12.
[19] Luceno, A. and Puig-Pey, J. (2000). ”Evaluationoftherun-length probability distribution for CUSUM charts: assessing chart performance”. Technometrics 42(4), pp. 411-416.
[20] Margavio, T. M.; Conerly, M. D.; Woodall, W. H.; and Drake, L. G. (1995). ”Alarm Rates for Quality Control Charts”. Statistics & Probability Letters 24(3), pp. 219-224.
[21] McCool, J. I. and Motley, T. J. (1998). ”Control Charts applicable when the fraction non- conforming is small”. Journal of Quality Technology 30, pp. 240-247.
[22] Mei, Y.; Han, S. W.; and Tsui, K-L. (2011). ”Early Detection of a Change in Poisson Rate after Accounting for Population Size Effects”. Statistica Sinica 21, pp. 597-624.
[23] Montgomery, D. C. (2009). Introduction to Statistical Quality Control, 7th Edition. Hobo- ken, NJ: John Wiley & Sons, Inc.
[24] Mousavi, S., and Reynolds, M.R., Jr. (2009). ”A CUSUM Chart for Monitoring a Pro- portion with Autocorrelated Binary Observations”. Journal of Quality Technology 41(4), pp. 401-414.
[25] Nelson, L. S. (1994). ”A control chart for parts-per-million nonconforming items”. Journal of Quality Technology, 26, pp. 239-240.
[26] Page, E. S. (1954). ”Continuous Inspection Schemes”. Biometrika 41, pp. 100-115.
[27] Pan, E. S.; Jin, Y.; Wang, S. Y.; and Cang, T. (2012). ”An Integrated EPQ Model based on a Control Chart for an Imperfect Production Process”. nternational Journal of Production Research 50(23), pp. 6999-7001.
[28] Perry, M. B. and Pignatiello, J. J. (2007). ”Change Point Estima- tion for Monotonically Changing Poisson Rates in SPC”. International Journal of Production Research 45(8), pp. 1791-1813.
[29] Perry, M. B. and Pignatiello, J. J. (2011). ”Estimating the Time of Step Change with Poisson CUSUM and EWMA Control Charts”. International Journal of Production Research 49(10), pp. 2857-2871.
[30] Quesenberry, C. P. (1991). ”SPC Q Charts for a Binomial Parameter p: Short or Long Runs”. Journal of Quality Technology 23(3), pp. 239-246.
[31] Quesenberry, C. P. (1995). ”Geometric Q charts for high quality pro- cesses”. Journal of Quality Technology 27(4), pp. 304-315.
[32] Quesenberry, C. P. (1995). ”On Properties of Binomial Q Charts for Attributes”. Journal of Quality Technology 27(3), pp. 204-213.
[33] Radaelli, G. (1994). ”Poisson and Negative Binomial Dynamics for Counted Data under CUSUM-type Charts”. Journal of Applied Statistics 21(5), pp. 347-356.
[34] Reynolds, M. R., Jr. and Stoumbos, Z. G. (1999). ”A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously”. Journal of Quality Technology 31(1), pp. 87-108. [35] Reynolds, M. R., Jr. and Stoumbos, Z.G. (2000). ”A General Approach to Modeling CUSUM Charts for a Proportion”. IIE Transactions 32(6), pp. 515-535.
[36] Saniga, E. M.; Davis, D. J.; and Lucas, J. M. (2009). ”Using Shewhart and CUSUM Charts for Diagnosis with Count data in a Vendor Certification Study”. Journal of Quality Technology 41(3), pp. 217-227.
[37] Sego, L. H.; Woodall, W. H.; and Reynolds, M. R. (2008). ”A Comparison of Surveillance Methods for Small Incidence Rates”. Statistics in Medicine 27(8), pp. 1225-1247.
[38] Shu, L.; Jiang, W.; and Tsui, K. L. (2008). ”A Weighted Cusum Chart for Detecting Pat- terned Mean Shifts”. Journal of Quality Technology 40(2), pp. 194-213.
[39] Shu, L.; Jiang, W.; and Tsui, K. L. (2011). ”A Comparison of Weighted CUSUM Procedures that Account for Monotone Changes in Population Size”. Statistics in Medicine 30(7), pp. 725- 741.
[40] Szarka, J. L. and Woodall, W. H. (2011). ”A Review and Perspec- tive on Surveillance of Bernoulli Processes”. Quality and Reliability Engineering Interna- tional 27(8), pp. 735-752. [41] Woodall, W. H. (1983). ”The distribution of the run length of one-sided CUSUM procedures for continuous random variables”. Technometrics 25(3), pp. 295-301.
[42] Woodall, W. H. (1997). ”ControlChartsbasedonAttributeData:Bibliography and Review”. Journal of Quality Technology 29, pp. 172-183.
[43] Wu, Z. and Jiao, J. X. (2008). ”A Control Chart for Monitoring Process Mean Based on Attribute Inspection”. International Journal of Production Research 46, pp. 4331-4347.
[44] Wu, Z.; Jiao, J. X.; and Liu, Y. (2008). ”A Binomial CUSUM Chart for Detecting Large Shifts in Fraction Nonconforming”. Journal of Applied Statistics 35(11), pp. 1267-1276.
[45] Wu, Z.; Yeo, S. H.; and Spedding, T. A. (2001). ”A Synthetic Control Chart for Detecting Fraction Nonconforming Increases”. Journal of Quality Technology 33(1), pp. 104-111.
[46] Yashchin, E. (1989). ”Weighted Cumulative Sum Technique”. Technometrics 31(3), pp. 321-338.
[47] Yashchin, E. (1993). ”Statistical Control Schemes: Methods, Applications and Generaliza- tions”. International Statistical Review 61(1), pp. 41-66.
[48] Yeha, A. B.; Mcgratha, R. N.; Sembowerb, M. A.; and Shen, Q. (2008). ”EWMA Control Charts for Monitoring High-yield Processes based on Nontransformed Observations”. Interna- tional Journal of Production Research 46(20), pp. 5679-5699.
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